• Substudy 1: Overall response rate (ORR) [ Time Frame: Until disease progression (up to 5 years) ]
  Overall response rate is defined as the percentage of participants with a confirmed complete response (CR) or partial response (PR) relative to the total number of participants within the analysis population at any time per Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1. as determined by the local investigators.
• Substudy 2: Overall response rate (ORR) [ Time Frame: Up to 5 years ]
  Overall response rate is defined as the percentage of participants with a confirmed CR or PR relative to the total number of participants within the analysis population at any time per RECIST v1.1. as assessed by central independent review.

• Substudy 1: Overall response rate [ Time Frame: Until disease progression (up to 5 years) ]
  Overall response rate is defined as the percentage of patients with a confirmed complete response (CR) or partial response (PR) relative to the total number of patients within the analysis population at any time as assessed by Investigators per Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1.
• Substudy 2: Overall response rate [ Time Frame: Up to 5 years ]
  Overall response rate is defined as the percentage of patients with a confirmed CR or PR relative to the total number of patients within the analysis population at any time as assessed by central independent review per RECIST v1.1.

• Substudy 1 and 2: Time to response [ Time Frame: Until disease progression (up to 5 years) ]
  Time to response is defined as time from date of T-cell administration to first documented evidence of confirmed (CR or PR) as assessed by local investigators per RECIST v1.1.
• Substudy 1 and 2: Duration of response (DOR) [ Time Frame: Until disease progression (up to 5 years) ]
  Duration of response is defined as, in the subset of participants who show a confirmed CR or PR as assessed by local investigators, the time from first documented evidence of CR or PR until the first documented sign of disease progression or death.
• Substudy 1 and 2: Disease control rate (DCR) [ Time Frame: Until disease progression (up to 5 years) ]
  Disease control rate is defined as the percentage of participants with a confirmed CR, PR, or stable disease (SD) with minimal 12 weeks duration relative to the total number of participants within the analysis population at the time of primary analysis as determined by Investigators per RECIST v1.1.
• Substudy 1 and 2: Progression free survival (PFS) [ Time Frame: Until disease progression (up to 5 years) ]
  Progression free survival is defined as the time from the date of T-cell administration until first documented sign of disease progression per RECIST v1.1, or death.
• Substudy 1 and 2: Frequency of adverse events (AEs), serious adverse events (SAEs) and AEs of special interest (AESI) according to severity [ Time Frame: Until disease progression (up to 5 years) ]
  AEs, SAEs and AESIs will be collected. Severity of AEs and SAEs will be summarized using NCI-CTCAE, version 5.0.
• Substudy 1 and 2: Number of participants with replication competent lentivirus (RCL) [ Time Frame: Until disease progression (up to 5 years) ]
  RCL exposure will be assessed by polymerase chain reaction (PCR) based assay.
• Substudy 1 and 2: Number of participants with insertional oncogenesis (IO) [ Time Frame: Until disease progression (up to 5 years) ]
  Peripheral blood mononuclear cells (PBMC) samples will be collected for monitoring insertional oncogenesis by PCR for gene modified cells in the blood.
• Substudy 2: Number of participants with clinically significant changes in hematology, clinical chemistry and urinalysis parameters [ Time Frame: Until disease progression (up to 5 years) ]
  Blood and urine samples will be collected for assessment of hematology, clinical chemistry and urinalysis parameters.
• Substudy 1 and 2: Maximum transgene expansion (Cmax) of letetresgene autoleucel [ Time Frame: Until disease progression (up to 5 years) ]
  Whole blood samples will be collected at indicated time points for evaluation of Cmax.
• Substudy 1 and 2: Time to Cmax (Tmax) [ Time Frame: Until disease progression (up to 5 years) ]
  Whole blood samples will be collected at indicated time points for evaluation of Tmax.
• Substudy 1 and 2: Area under the concentration/persistence time curve from zero to time t (AUC[0-t]) [ Time Frame: Until disease progression (up to 5 years) ]
  Whole blood samples will be collected at indicated time points for evaluation of AUC(0-t).
• Substudy 2: Overall response rate (ORR) [ Time Frame: Up to 5 years ]
  Overall response rate is defined as the percentage of participants with a confirmed CR or PR relative to the total number of participants within the analysis population at any time per RECIST v1.1. as determined by the local investigators.
• Substudy 2: Overall Survival (OS) [ Time Frame: Up to 5 years ]
  Overall Survival is defined as the interval of time between the date of T-cell infusion and the date of death.
• Substudy 2: Number of participants with positive anti-drug antibodies (ADA) and titers of ADA against letetresgene autoleucel [ Time Frame: Up to 36 months ]
  Serum samples will be collected to analyze for the presence of ADAs using validated immunoassays.

• Substudy 1: Time to response [ Time Frame: Until disease progression (up to 5 years) ]
  Time to response is the time from the date of T-cell infusion to initial date of confirmed response (PR or CR) as assessed by Investigators per RECIST v1.1 in the subset of patients who achieved a confirmed PR or CR.
• Substudy 1: Duration of response [ Time Frame: Until disease progression (up to 5 years) ]
  Duration of response is defined as, in the subset of patients who show a confirmed CR or PR as assessed by Investigators per RECIST v1.1, the time from first documented evidence of CR or PR until the first documented sign of disease progression or death.
• Substudy 1: Disease control rate [ Time Frame: Until disease progression (up to 5 years) ]
  Disease control rate is defined as the percentage of patients with a confirmed CR, PR, or stable disease (SD) with minimal 12 weeks duration relative to the total number of patients within the analysis population at the time of primary analysis as determined by Investigators per RECIST v1.1.
• Substudy 1: Progression free survival [ Time Frame: Until disease progression (up to 5 years) ]
  Progression free survival is defined as the time from the date of T-cell infusion until the earliest date of radiological progression of disease (PD) as assessed by the Investigator per RECIST v1.1, or death due to any cause.
• Substudy 1: Number of patients with adverse events (AEs) and serious adverse events (SAEs) [ Time Frame: Until disease progression (up to 5 years) ]
  An AE is any untoward medical occurrence in a clinical study patient, temporally associated with the use of a study intervention, whether or not considered related to the study intervention. SAE is any untoward medical occurrence that, at any dose results in death, is life-threatening, requires hospitalization or prolongation of existing hospitalization, results in persistent disability/incapacity is a congenital anomaly/birth defect or any other situation as per Medical or scientific judgment.
• Substudy 1: Severity and duration of adverse events of special interest (AESIs) [ Time Frame: Until disease progression (up to 5 years) ]
  To assess the AESIs as a criteria of safety.
• Substudy 1: Number of patients with replication competent lentivirus (RCL) [ Time Frame: Until disease progression (up to 5 years) ]
  RCL exposure will be assessed by polymerase chain reaction (PCR) based assay.
• Substudy 1: Number of patients with insertional oncogenesis [ Time Frame: Until disease progression (up to 5 years) ]
  Peripheral blood mononuclear cells (PBMC) samples will be collected for monitoring insertional oncogenesis by PCR for gene modified cells in the blood.
• Substudy 1: Change from Baseline in hematology parameters: platelets [ Time Frame: Baseline and until disease progression (up to 5 years) ]
  Blood samples will be collected for analysis of hematology parameters.
• Substudy 1: Change from Baseline in hematology parameters: hematocrit [ Time Frame: Baseline and until disease progression (up to 5 years) ]
  Blood samples will be collected for analysis of hematology parameters.
• Substudy 1: Change from Baseline in hematology parameters: hemoglobin [ Time Frame: Baseline and until disease progression (up to 5 years) ]
  Blood samples will be collected for analysis of hematology parameters.
• Substudy 1: Change from Baseline in hematology parameters: Red blood cell (RBC) count [ Time Frame: Baseline and until disease progression (up to 5 years) ]
  Blood samples will be collected for analysis of hematology parameters.
• Substudy 1: Change from Baseline in hematology parameters: White blood cell (WBC) count [ Time Frame: Baseline and until disease progression (up to 5 years) ]
  Blood samples will be collected for analysis of hematology parameters.
• Substudy 1: Change from Baseline in clinical chemistry parameters: Alkaline Phosphatase, Alanine Aminotransferase (ALT), and Aspartate Aminotransferase (AST) [ Time Frame: Baseline and until disease progression (up to 5 years) ]
  Blood samples will be collected for analysis of clinical chemistry parameters.
• Substudy 1: Change from Baseline in clinical chemistry parameters: Blood Urea Nitrogen (BUN) [ Time Frame: Baseline and until disease progression (up to 5 years) ]
  Blood samples will be collected for analysis of clinical chemistry parameters.
• Substudy 1: Change from Baseline in clinical chemistry parameters: Total and Direct bilirubin, Creatinine [ Time Frame: Baseline and until disease progression (up to 5 years) ]
  Blood samples will be collected for analysis of clinical chemistry parameters.
• Substudy 1: Change from Baseline in urine parameters: potential of hydrogen (pH) [ Time Frame: Baseline and up to day -4 ]
  Urine samples will be collected for analysis of urine parameters.
• Substudy 1: Change from Baseline in urine parameters: glucose, protein, blood, bilirubin [ Time Frame: Baseline and up to day -4 ]
  Urine samples will be collected for analysis of urine parameters.
• Substudy 1: T Cell Persistence of GSK3377794 [ Time Frame: Until disease progression (up to 5 years) ]
  Blood samples will be collected for T Cell Persistence analysis of GSK3377794 transduced cell quantities.
• Substudy 2: Time to response [ Time Frame: Up to 5 years ]
  Time to response is the time from the date of T-cell infusion to initial date of confirmed response (PR or CR) as assessed by independent central review per RECIST v1.1 in the subset of patients who achieved a confirmed PR or CR.
• Substudy 2: Duration of response [ Time Frame: Up to 5 years ]
  Duration of response is defined as, in the subset of patients who show a confirmed CR or PR as assessed by independent central review per RECIST v1.1, the time from first documented evidence of CR or PR until the first documented sign of disease progression or death.
• Substudy 2: Disease control rate [ Time Frame: Up to 5 years ]
  Disease control rate is defined as the percentage of patients with a confirmed CR, PR, or SD with minimal 12 weeks duration relative to the total number of patients within the analysis population at the time of primary analysis as determined by independent central review per RECIST v1.1.
• Substudy 2: Progression free survival [ Time Frame: Up to 5 years ]
  Progression free survival is defined as the time from the date of T-cell infusion until the earliest date of radiological PD as assessed by the independent central review per RECIST v1.1, or death due to any cause.
• Substudy 2: Overall survival [ Time Frame: Up to 5 years ]
  Overall survival is defined as the interval of time between the date of T-cell infusion and the date of death due to any cause.
• Substudy 2: Number of patients with AEs and SAEs [ Time Frame: Up to 5 years ]
  An AE is any untoward medical occurrence in a clinical study patient, temporally associated with the use of a study intervention, whether or not considered related to the study intervention. SAE is any untoward medical occurrence that, at any dose results in death, is life-threatening, requires hospitalization or prolongation of existing hospitalization, results in persistent disability/incapacity is a congenital anomaly/birth defect or any other situation as per Medical or scientific judgment.
• Substudy 2: Severity and duration of adverse events of special interest (AESIs) [ Time Frame: Up to 5 years ]
  To assess the AESIs as a criteria of safety.
• Substudy 2: Number of patients with RCL [ Time Frame: Up to 5 years ]
  RCL exposure will be assessed by PCR based assay.
• Substudy 2: Number of patients with insertional oncogenesis [ Time Frame: Up to 5 years ]
  PBMC samples will be collected for monitoring insertional oncogenesis by PCR for gene modified cells in the blood.
• Substudy 2: Number of patients with positive anti-drug antibodies (ADA) against GSK3377794 [ Time Frame: Up to 36 months ]
  Serum samples will be collected up to 36 months for ADA test.
• Substudy 2: Titers of ADA against GSK3377794 [ Time Frame: Up to 36 months ]
  Serum samples will be collected to analyze for the presence of ADAs using validated immunoassays.
• Substudy 2: Change from Baseline in hematology parameters: platelets [ Time Frame: Baseline and up to 5 years ]
  Blood samples will be collected for analysis of hematology parameters.
• Substudy 2: Change from Baseline in hematology parameters: hematocrit [ Time Frame: Baseline and up to 5 years ]
  Blood samples will be collected for analysis of hematology parameters.
• Substudy 2: Change from Baseline in hematology parameters: hemoglobin [ Time Frame: Baseline and up to 5 years ]
  Blood samples will be collected for analysis of hematology parameters.
• Substudy 2: Change from Baseline in hematology parameters: Red blood cell (RBC) count [ Time Frame: Baseline and up to 5 years ]
  Blood samples will be collected for analysis of hematology parameters.
• Substudy 2: Change from Baseline in hematology parameters: White blood cell (WBC) count [ Time Frame: Baseline and up to 5 years ]
  Blood samples will be collected for analysis of hematology parameters.
• Substudy 2: Change from Baseline in clinical chemistry parameters: Alkaline Phosphatase, Alanine Aminotransferase (ALT), and Aspartate Aminotransferase (AST) [ Time Frame: Baseline and up to 5 years ]
  Blood samples will be collected for analysis of clinical chemistry parameters.
• Substudy 2: Change from Baseline in clinical chemistry parameters: Blood Urea Nitrogen (BUN) [ Time Frame: Baseline and up to 5 years ]
  Blood samples will be collected for analysis of clinical chemistry parameters.
• Substudy 2: Change from Baseline in clinical chemistry parameters: Total and Direct bilirubin, Creatinine [ Time Frame: Baseline and up to 5 years ]
  Blood samples will be collected for analysis of clinical chemistry parameters.
• Substudy 2: Change from Baseline in urine parameters: potential of hydrogen (pH) [ Time Frame: Baseline and up to day -4 ]
  Urine samples will be collected for analysis of urine parameters.
• Substudy 2: Change from Baseline in urine parameters: glucose, protein, blood, bilirubin [ Time Frame: Baseline and up to day -4 ]
  Urine samples will be collected for analysis of urine parameters.
• Substudy 2: T Cell Persistence of GSK3377794 [ Time Frame: Up to 5 years ]
  Blood samples will be collected for T Cell Persistence analysis of GSK3377794 transduced cell quantities.

• Drug: letetresgene autoleucel (lete-cel, GSK3377794)
  letetresgene autoleucel will be administered.
• Drug: Fludarabine
  Fludarabine will be used as the lymphodepleting chemotherapy
• Drug: Cyclophosphamide
  Cyclophosphamide will be used as the lymphodepleting chemotherapy.

• Experimental: Substudy 1: lete-cel in previously untreated advanced (metastatic or unresectable) SS or MRCLS
  Eligible participants will be leukapheresed to manufacture engineered T cells. Participants will then receive letetresgene autoleucel.
  Interventions:

  • Drug: letetresgene autoleucel (lete-cel, GSK3377794)
  • Drug: Fludarabine
  • Drug: Cyclophosphamide
• Experimental: Substudy 2: lete-cel in advanced (metastatic or unresectable) SS or MRCLS post anthracycline chemo
  Eligible participants will be leukapheresed to manufacture engineered T cells. Participants will then receive letetresgene autoleucel.
  Interventions:

  • Drug: letetresgene autoleucel (lete-cel, GSK3377794)
  • Drug: Fludarabine
  • Drug: Cyclophosphamide

Inclusion Criteria:

• Participant must be greater than or equal to 10 years of age on the day of signing informed consent.
• Participant must be positive for HLA-A*02:01, HLA-A*02:05, and/or HLA-A*02:06 alleles by a designated central laboratory
• Participant's tumor is positive for NY-ESO-1 expression by a designated central laboratory.
• Participant has a diagnosis of synovial sarcoma (SS) or myxoid/round cell liposarcoma (MRCLS) confirmed by local histopathology Specifics requirements per substudy.
• Performance status: dependent on age - Lansky > 60, Karnofsky > 60, Eastern Cooperative Oncology Group 0-1.
• Participant must have adequate organ function and blood cell counts, within 7 days prior to leukapheresis.
• At time of treatment, participant has measurable disease according to RECIST v1.1.

Exclusion Criteria:

• Central nervous system metastases.
• Any other prior malignancy that is not in complete remission.
• Clinically significant systemic illness.
• Prior or active demyelinating disease.
• History of chronic or recurrent (within the last year prior to leukapheresis) severe autoimmune or immune mediated disease (e.g. Crohn's disease, systemic lupus) requiring steroids or other immunosuppressive treatments.
• Previous treatment with genetically engineered NY-ESO-1-specific T cells.
• Previous NY-ESO-1 vaccine or NY-ESO-1 targeting antibody.
• Prior gene therapy using an integrating vector.
• Previous allogeneic hematopoietic stem cell transplant.
• Washout periods for prior radiotherapy and systemic chemotherapy must be followed.
• Participant had major surgery in less than or equal to 28 days of first dose of study intervention.