A Study of TAK-659 in Combination With Venetoclax for Adult Participants With Previously Treated Non-Hodgkin Lymphoma

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.