The purpose of this study is to determine the maximum tolerated dose (MTD) and/or recommended phase 2 dose (RP2D) of TAK-659 and venetoclax when administered in combination in participants with non-Hodgkin lymphoma (NHL) relapsed and/or refractory after at least 1 prior line of therapy and to evaluate safety and tolerability of TAK-659 and venetoclax when administered in combination.

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.

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.

Takeda provides access to the de-identified individual participant data (IPD) for eligible studies to aid qualified researchers in addressing legitimate scientific objectives (Takeda's data sharing commitment is available on https://clinicaltrials.takeda.com/takedas-commitment?commitment=5). These IPDs will be provided in a secure research environment following approval of a data sharing request, and under the terms of a data sharing agreement.

IPD from eligible studies will be shared with qualified researchers according to the criteria and process described on https://vivli.org/ourmember/takeda/. For approved requests, the researchers will be provided access to anonymized data (to respect patient privacy in line with applicable laws and regulations) and with information necessary to address the research objectives under the terms of a data sharing agreement.