• Number of Participants with a Dose Limiting Toxicity (DLT) [ Time Frame: Baseline up to 5 weeks ]
  Toxicity will be evaluated according to National Cancer Institute Common Terminology Criteria for Adverse Event (NCI CTCAE), Version 5.0 DLT will be defined as any of the events specified in the protocol that are considered by the investigator to be at least possibly related to therapy with study medications and that occur within the first cycle.
• Percentage of Participants Reporting one or More Treatment-emergent Adverse Events (TEAEs), Grade 3 or Higher Adverse Events (AEs), Serious Adverse Events (SAEs) and AEs Leading to Discontinuation [ Time Frame: Baseline up to 13 months ]
  AE Grades will be evaluated as per NCI CTCAE, version 5.0.

• Percentage of Participants Reporting one or More Treatment-emergent Adverse Events (TEAEs) [ Time Frame: Baseline up to 13 months ]
• Percentage of Participants with Grade 3 or Higher Adverse Events (AEs) [ Time Frame: Baseline up to 13 months ]
  AE Grades will be evaluated as per National Cancer Institute Common Terminology Criteria for Adverse Event (NCI CTCAE), version 4.03. Grade 1 scaled as Mild; Grade 2 scaled as Moderate; Grade 3 scaled as severe or medically significant but not immediately life-threatening; Grade 4 scaled as life-threatening consequences; and Grade 5 scaled as death related to AE.
• Percentage of Participants with Drug Related AEs [ Time Frame: Baseline up to 13 months ]
• Percentage of Participants with Drug Related Grade 3 or Higher AEs [ Time Frame: Baseline up to 13 months ]
  AE Grades will be evaluated as per NCI CTCAE, version 4.03. Grade 1 scaled as Mild; Grade 2 scaled as Moderate; Grade 3 scaled as severe or medically significant but not immediately life-threatening; Grade 4 scaled as life-threatening consequences; and Grade 5 scaled as death related to AE.
• Percentage of Participants Reporting One or More Serious Adverse Events (SAEs) [ Time Frame: Baseline up to 13 months ]
• Percentage of Participants with AEs Leading to Discontinuation [ Time Frame: Baseline up to 13 months ]
• Number of Participants with a Dose Limiting Toxicity (DLT) [ Time Frame: Baseline up to 8 weeks ]
  Toxicity will be evaluated according to NCI CTCAE, Version4.03. DLT will be defined as any of the events specified in the protocol that are considered by the investigator to be at least possibly related to therapy with study medications.
• Percentage of Participants with Clinically Significant Laboratory Abnormalities [ Time Frame: Baseline up to 13 months ]
• Percentage of Participants with Clinically Significant Vital Sign Abnormalities [ Time Frame: Baseline up to 13 months ]

• Cmax: Maximum Observed Plasma Concentration for TAK-659 and Venetoclax [ Time Frame: Cycle 1 Days 1 and 21 or 28: Pre-dose and at multiple time points (up to 24 hours) post-dose (Cycle length is equal to [=] 35 days) ]
• Tmax: Time to Reach the Maximum Plasma Concentration (Cmax) for TAK-659 and Venetoclax [ Time Frame: Cycle 1 Days 1 and 21 or 28: Pre-dose and at multiple time points (up to 24 hours) post-dose (Cycle length =35 days) ]
• AUCτ: Area Under the Plasma Concentration-time Curve from Time 0 to Time Over the Dosing Interval for TAK-659 and Venetoclax [ Time Frame: Cycle 1 Days 1 and 21 or 28: Pre-dose and at multiple time points (up to 24 hours) post-dose (Cycle length =35 days) ]
• Oral Clearance (CL/F) for TAK-659 and Venetoclax [ Time Frame: Cycle 1 Days 1 and 21 or 28: Pre-dose and at multiple time points (up to 24 hours) post-dose (Cycle length =35 days) ]
• Peak-trough Ratio (PTR) for TAK-659 and Venetoclax [ Time Frame: Cycle 1 Days 1 and 21 or 28: Pre-dose and at multiple time points (up to 24 hours) post-dose (Cycle length =35 days) ]
• Accumulation Ratio (Rac) for TAK-659 and Venetoclax [ Time Frame: Cycle 1 Days 1 and 21 or 28: Pre-dose and at multiple time points (up to 24 hours) post-dose (Cycle length =35 days) ]
• Trough Concentration (C trough) for TAK-659 and Venetoclax [ Time Frame: Cycle 1 Days 1 and 21 or 28: Pre-dose and at multiple time points (up to 24 hours) post-dose (Cycle length =35 days) ]
• Overall Response Rate (ORR) [ Time Frame: Up to 12 months ]
  ORR is calculated as percentage of participants with complete response (CR) + percentage of participants with partial response (PR) as assessed by International Working Group (IWG) criteria for malignant lymphoma.
• Duration of Overall Response [ Time Frame: Up to 12 months ]
• CR Rate [ Time Frame: Up to 12 months ]
  CR rate is calculated as percentage of participants with CR as assessed by IWG criteria for malignant lymphoma.
• Duration of CR [ Time Frame: Up to 12 months ]
• Time to Progression (TTP) [ Time Frame: Up to 13 months ]
  TTP will be measured as the time in months from the first dose of study treatment to the date of the first documented disease progression as assessed using IWG criteria.
• Progression-free Survival (PFS) [ Time Frame: Up to 18 months ]
  PFS is defined as the time from date of first study drug administration to the day of first documented disease progression or death due to any cause, whichever occurs first.

• Cmax: Maximum Observed Plasma Concentration for TAK-659 and Venetoclax [ Time Frame: Cycle 1 Days 1 and 28: Pre-dose and at multiple time points (up to 24 hours) post-dose ]
• Tmax: Time to Reach the Maximum Plasma Concentration (Cmax) for TAK-659 and Venetoclax [ Time Frame: Cycle 1 Days 1 and 28: Pre-dose and at multiple time points (up to 24 hours) post-dose ]
• AUCτ: Area Under the Plasma Concentration-time Curve from Time 0 to Time Over the Dosing Interval for TAK-659 and Venetoclax [ Time Frame: Cycle 1 Days 1 and 28: Pre-dose and at multiple time points (up to 24 hours) post-dose ]
• Oral Clearance (CL/F) for TAK-659 and Venetoclax [ Time Frame: Cycle 1 Day 28: Pre-dose and at multiple time points (up to 24 hours) post-dose ]
• Peak-trough Ratio (PTR) for TAK-659 and Venetoclax [ Time Frame: Cycle 1 Day 28: Pre-dose and at multiple time points (up to 24 hours) post-dose ]
• Accumulation Ratio (Rac) for TAK-659 and Venetoclax [ Time Frame: Cycle 1 Day 28: Pre-dose and at multiple time points (up to 24 hours) post-dose ]
• Trough Concentration (C trough) for TAK-659 and Venetoclax [ Time Frame: Cycle 1 Day 28: Pre-dose and at multiple time points (up to 24 hours) post-dose ]
• Overall Response Rate (ORR) [ Time Frame: Up to 12 months ]
  ORR is calculated as percentage of participants with complete response (CR) + percentage of participants with partial response (PR) as assessed by International Working Group (IWG) criteria for malignant lymphoma.
• Duration of Overall Response [ Time Frame: Up to 12 months ]
• Complete Response (CR) Rate [ Time Frame: Up to 12 months ]
  CR rate is calculated as percentage of participants with complete response (CR) as assessed by IWG criteria for malignant lymphoma.
• Duration of CR [ Time Frame: Up to 12 months ]
• Time to Progression (TTP) [ Time Frame: Up to 13 months ]
  TTP will be measured as the time in months from the first dose of study treatment to the date of the first documented progressive disease (PD) as assessed using IWG criteria.

The drugs being tested in this study are called TAK-659 and venetoclax. TAK-659 in combination with venetoclax is being tested to treat people who have advanced NHL after at least 1 prior line of therapy. This study will look at the safety data, pharmacokinetic (PK) data and any early anti-tumor activity observed.

The study will enroll approximately 53 participants.

• TAK-659 and venetoclax doses will be escalated according to a Bayesian logistic regression model (BLRM) with overdose control escalation schema. TAK-659 60 mg + Venetoclax 400 mg is the starting dose.

Participants could also receive 40 mg, 60 mg, 80 mg or 100 mg TAK-659 during dose escalation and 200 mg, 400 mg, 800 mg, or 1200 mg of venetoclax.

Following dose escalation the safety and tolerability of the MTD/RP2D of the TAK-659+venetoclax combination will be further explored in two dose-safety expansion cohorts, Cohort A in participants with DLBCL and Cohort B in participants with FL.

All participants will be asked to take one tablet of TAK-659 on an empty stomach at least 1 hour before and no sooner than 2 hours after eating food and/or drinking fluids other than water. Venetoclax will be taken with a meal and water 2 hours after TAK-659 has been taken. No food or drink (except water) are allowed between TAK-659 and venetoclax. TAK-659 and venetoclax should be taken at the same time each day throughout the study.

This multi-center trial will be conducted in the United States, Canada and Europe. The overall time to participate in this study is 20 months or until disease progression, unacceptable toxicities, or withdrawal from study by participant. Participants will make multiple visits to the clinic, and will be followed for 28 days (+10) days after the last dose of TAK-659 or venetoclax or the start of subsequent alternative anticancer therapy to permit the detection of any delayed treatment-related AEs. For participants enrolled in either the dose escalation or safety expansion phases, the maximum duration of treatment will be 12 months unless, in the opinion of the investigator and with the agreement of the sponsor, the participant would derive benefit from continued therapy beyond 12 months. Participants enrolled in the safety expansion part who stop treatment for any reason other than disease progression will continue PFS follow-up every 2 months after the last dose of study drug for up to 6 months or until disease progression or the start of alternative therapy, whichever occurs first.

• Lymphoma, Non-Hodgkin
• Lymphoma, Large B-cell, Diffuse
• Lymphoma, Follicular

• Drug: TAK-659
  TAK-659 tablets.
• Drug: Venetoclax
  Venetoclax tablets.

• Experimental: Dose Escalation: TAK-659 + Venetoclax
  TAK-659 40, 60, 80, or 100 milligram (mg) (tablet, orally, once daily, up to 35 days in Cycle 1 or in different intermittent schedules [7 days dosing followed by 7 days off or 14 days dosing followed by 7 days off or other intermittent dosing schedules]) along with venetoclax 200, 400, 800 or 1200 mg (tablet, orally, once daily, up to 35 days in Cycle 1). After Cycle 1, TAK-659 and venetoclax will be administered once daily in a 28-day treatment cycle until disease progression, unacceptable toxicities, or discontinuation by participant.
  Interventions:

  • Drug: TAK-659
  • Drug: Venetoclax
• Experimental: Safety Expansion: Diffuse Large B-cell Lymphoma (DLBCL) Cohort
  TAK-659 tablet, orally, once daily along with venetoclax tablet, orally, once daily in a 28-day treatment cycle until disease progression, unacceptable toxicities, or discontinuation by participant. TAK-659 and venetoclax MTD/RP2D will be determined from the dose escalation phase.
  Interventions:

  • Drug: TAK-659
  • Drug: Venetoclax
• Experimental: Safety Expansion: Follicular Lymphoma (FL) Cohort
  TAK-659 tablet, orally, once daily along with venetoclax tablet, orally, once daily in a 28-day treatment cycle until disease progression, unacceptable toxicities, or discontinuation by participant. TAK-659 and venetoclax MTD/RP2D will be determined from the dose escalation phase.
  Interventions:

  • Drug: TAK-659
  • Drug: Venetoclax

Inclusion Criteria:

1. For the Dose Escalation phase, participants must have histologically confirmed diagnosis of advanced NHL of any histology (with the exception of participants with mantle cell lymphoma [MCL] or chronic lymphoma leukemia [CLL]).
2. For the Safety Expansion phase, participants must have histologically confirmed diagnosis of advanced DLBCL or FL.
3. Radiographically or clinically measurable disease with greater than or equal to (>=) 1 target lesion per IWG criteria for malignant lymphoma.

4. Refractory or relapsed after at least 1 prior line of therapy for whom no effective standard therapy is available per investigator's assessment.

   o Participants who are either treatment-naive to, relapsed after, or refractory to ibrutinib, idelalisib, or any other investigational B cell receptor (BCR) pathway inhibitors not directly targeting spleen tyrosine kinase (SYK) are allowed.

5. Eastern Cooperative Oncology Group (ECOG) performance status score of 0 or 1.
6. Life expectancy of greater than 3 months.
7. Suitable venous access for the study-required blood sampling that is, including PK and pharmacodynamic sampling.
8. Recovered (that is, less than or equal to [<=] Grade 1 toxicity) from the reversible effects of prior anticancer therapy.

Exclusion Criteria:

1. Central nervous system (CNS) lymphoma; active brain or leptomeningeal metastases, as indicated by positive cytology from lumbar puncture or computed tomography (CT) scan/magnetic resonance imaging (MRI).
2. History of drug-induced pneumonitis requiring treatment with steroids; history of idiopathic pulmonary fibrosis, organizing pneumonia, or evidence of active pneumonitis on screening chest CT scan; history of radiation pneumonitis in the radiation field (fibrosis) is permitted.
3. Participants requires the use of warfarin (use in prophylactic doses [example, deep vein thrombosis prophylaxis]) is allowed.
4. Prior exposure to targeted SYK inhibitors.
5. History of a prior intolerable toxicity, in the opinion of the investigator from another B-cell lymphoma (BCL)-2 family protein inhibitor study.
6. Participants who are relapsed after or refractory to regimens containing venetoclax or other BCL2 inhibitors.
7. Systemic anticancer treatment (including investigational agents) or radiotherapy less than 2 weeks before the first dose of study treatment (<=4 weeks for large molecule agents; <=8 weeks for cell-based therapy or anti-tumor vaccine), or not recovered from the reversible effects of prior anticancer therapy.
8. Prior autologous stem cell transplant (ASCT) within 6 months preceding Cycle 1 Day 1.
9. Prior allogeneic stem cell transplant and/or chimeric antigen receptor T-cell therapy at any time.
10. Major surgery within 14 days before the first dose of study drug and not recovered fully from any complications from surgery.
11. Known human immunodeficiency virus (HIV) positive or HIV-related malignancy.
12. Received a live viral vaccine within 6 months prior to the first dose of study drug.

13. Use or consumption of:

    • Medications or supplements that are known to be strong or moderate Cytochrome P4503A (CYP3A) inhibitors or strong or moderate CYP3A inducers and/or P-glycoprotein (P-gp) inhibitors or inducers within 7 days or within 5 times the inhibitor or inducer half-life (whichever is longer) before the first dose of study drugs. In general, the use of these agents is not permitted during the study except in cases in which an adverse event (AE) must be managed during interruption of study drug dosing.
    • Food or beverages containing grapefruit, Seville oranges, or Star fruit within 5 days before the first dose of study drugs. Note that food and beverages containing grapefruit, Seville orange, or Star fruit are not permitted during the study.
    • Preparations containing St. John's wort within 7 days before the first dose of study drugs. Note that preparations containing St. John's wort are not permitted during the study.