• Number of participants with treatment-related adverse events as assessed by CTCAE v5.0 [ Time Frame: 24 months ]
• Overall remission rate (ORR) [ Time Frame: 3 months ]

• Response at Day 28±3 days [ Time Frame: 1 month ]
• Percentage of patients who achieve complete remission (CR) or complete remission with incomplete blood count recovery (CRi) (partial remission，PR) at month 6 without SCT between CNCT19 infusion and Month 6 response assessment. [ Time Frame: 6 months ]
• Percentage of patients who achieve CR or CRi (PR) with minimal residual disease negative bone marrow. [ Time Frame: 6 months ]
• Relapse-free survival [ Time Frame: 24 months ]
• Progression-free survival [ Time Frame: 24 months ]
• Percentage of patients who achieve best overall response (BOR) [ Time Frame: 24 months ]
• Duration of remission (DOR) [ Time Frame: 24 months ]
• Overall survival [ Time Frame: 24 months ]
• Percentage of patient who achieve CR or CRi (PR) and then proceed to stem cell transplantation（SCT） while in remission. [ Time Frame: 24 months ]
• Proportion of patients with detectable replication competent lentivirus (RCL) by vesicular stomatitis virus, glycoprotein (VSV-G) [ Time Frame: at Month 3 post treatment then Month 6 and Month12, yearly until year 15 if CD19 chimeric antigen receptor (CAR) transgene is still detected ]

Inclusion Criteria:

1. Informed consent is signed by a subject or his lineal relation.
2. Age 18 or older.

3. Relapsed or refractory B-cell lineage acute lymphoblastic leukemia (B-ALL)

   • Relapsed or refractory

     • Relapse within 12 months of first remission
     • Without remission after 2 cycles of induction chemotherapy regimen.
     • Without remission after more than 6 weeks of induction chemotherapy.
     • 2nd or greater Bone Marrow (BM) relapse
     • Any BM relapse after autologous/allogeneic stem cell transplantation (SCT)
   • documentation of cluster of differentiation 19 (CD19) tumor expression demonstrated in bone marrow or peripheral blood within 3 months of study entry.
   • Patients with Philadelphia chromosome positive (Ph+) ALL are eligible if they are intolerant to or have failed 1generation and/or 2 generation of tyrosine kinase inhibitor therapy (TKI); no TKI salvage treatments if the patient has a BCR-ABL1 kinase domain gatekeeper mutation Thr315Ile (T315I) mutation.
   • Bone marrow with ≥ 5% lymphoblasts by morphologic assessment or minimal residual disease (MRD) positive at screening

4. Relapsed or refractory B-cell non-Hodgkin's lymphoma (NHL) with CD19-positive after two systemic lines of therapy

   • Chemotherapy-refractory disease, defined as one of more of the following:

     • No response to last line of therapy. i. Progressive disease (PD) as best response to most recent therapy regimen. ii. Stable disease (SD) as best response to most recent therapy with duration no longer than 6 month from last dose of therapy

     • Refractory post-autologous stem cell transplant (ASCT) or allogeneic stem cell transplantation (allo-HSCT).

       i. Disease progression or relapsed less than or equal to 12 months of ASCT /allo-HSCT (must have biopsy proven recurrence in relapsed individuals).

   ii. If salvage therapy is given post-ASCT, the individual must have had no response to or relapsed after the last line of therapy Any BM relapse after autologous/allogeneic stem cell transplantation (SCT).

   • Individuals must have received two systemic lines of therapy

     • anti-cluster of differentiation 20 (CD20) monoclonal antibody unless investigator determines that tumor is CD20-negative and
     • an anthracycline containing chemotherapy regimen

5. Relapsed or refractory chronic lymphocytic leukemia (CLL) with CD19-positive Diagnosis of CLL that meets 2008 the International Workshop on Chronic Lymphocytic Leukemia (IWCLL) diagnostic criteria, must have at least one of the following criteria.

   • Patients with Del(17p) / tumour suppressor p53 (TP53) mutation
   • CLL relapsed or refractory after 2 or more lines of therapy, Relapsed is defined as evidence of disease progression after a period of 6 months or more following an initial CR or PR.

   Refractory disease is defined as failure to achieve a response after 6 cycles of induction chemotherapy or having disease progression within 6 months of the last treatment.

6. At least one measurable lesion, defined as at least 1 lymph node >1.5 cm in the longest diameter, per revised IWG Response Criteria.
7. Eastern cooperative oncology group (ECOG) performance status of 0 to 2.

8. Adequate organ function defined as:

   • Serum alanine aminotransferase (ALT)/aspartate aminotransferase (AST) ≤3 upper limit of normal (ULN)
   • Total bilirubin ≤ 2 ULN, except in individuals with Gilbert's syndrome; Note: Patients with Gilbert's syndrome that bilirubin ≤ 3 ULN and direct bilirubin ≤ 1.5 ULN will be eligible.
   • A serum creatinine≤ 1.5 ULN or Creatine removal rate ≥ 60mL/min（Cockcroft and Gault）
   • Must have a minimum level of pulmonary reserve as ≤ Grade 1 dyspnea and oxygen saturation > 91% on room air.
   • International normalized ratio (INR) ≤ 1.5 ULN and activated partial thromboplastin time (APTT) ≤ 1.5 ULN.
9. Women of child-bearing potential and all male participants must use highly effective methods of contraception for a period of 1 year after the CNCT19 infusion.

Exclusion Criteria:

1. Active central nervous system (CNS) involvement by malignancy.
2. Patients with systemic vasculitis (such as Wegener granulomatosis, nodular polyarteritis, systemic lupus erythematosus) and active or uncontrolled autoimmune disease (such as autoimmune hemolytic anemia, etc.)
3. Patients who are positive for any of HIV antibody, TP antibody, hepatitis B surface antigen (HBsAg) and hepatitis C virus (HCV) antibody.
4. During the first four weeks of screening, the patient underwent major surgery which was assessed by the investigator as unsuitable for enrollment;

5. The patient's heart fits any of the following conditions:

   Left Ventricular Ejection Fraction (LVEF) ≤45%; III/IV congestive heart failure (NYHA); Severe arrhythmia (except for Atrial fibrillation, Paroxysmal supraventricular tachycardia); corrected QT interval (QTc)≥450ms (male)or QTc≥470ms (female)（QTc using Bazett's(QTcB)=QT/RR^0.5）; Myocardial infarction or Coronary Artery Bypass Graft Surgery, heart stent surgery.

   Other heart diseases that have been judged by the investigator to be unsuitable for receiving cell therapy.

6. Patients with a history of epilepsy or other active central nervous system diseases.
7. Has had treat with live vaccine within 6 weeks prior to screening；
8. Patients with evidence of currently uncontrollable serious active infections (e.g., sepsis, bacteremia, fungemia, viremia, etc.).
9. Life expectancy < 12 weeks.
10. Patients with other conditions making the patients unsuitable for receiving cell therapy as judged by the investigator.