A Study of TAK-659 as a Single Agent in Adult East Asian Participants With Non-Hodgkin Lymphoma (NHL)

Inclusion Criteria: 1. To be enrolled to the dose escalation part, participants must have histologically or cytologically confirmed diagnosis of NHL for which no effective standard treatment is available. 2. To be enrolled in the expansion part, participants must meet the following criteria: 1. Must have pathologically confirmed FL (Grade 1, 2, or 3A) or MZL. 2. Relapsed and/or refractory to \>=2 prior lines of chemotherapy based on standard of care that include at least 1 anti-CD20-based regimen, as well as alkylating agents (example cyclophosphamide or bendamustine). 3. Participants must be ineligible for or refusal to hematopoietic stem cell transplant. 4. If the participants have relapsed or progressed after achieving a response (defined as CR or PR), documented, investigator-assessed relapse or progression after the last treatment is required. 3. Measurable disease per IWG 2007 criteria. 4. Eastern Cooperative Oncology Group performance status score of 0 or 1. 5. Life expectancy of longer than 3 months. 6. Adequate organ function, including the following: 1. Bone marrow reserve: absolute neutrophil count \>=1,000 per cubic millimeter (/mm\^3), platelet count \>=75,000/mm\^3 (\>=50,000/mm\^3 for participants with bone marrow involvement), and hemoglobin \>=8 gram per deciliter (g/dL) (red blood cell \[RBC\] and platelet transfusion allowed \>=14 days before assessment). 2. Hepatic function: total bilirubin less than or equal to (\<=) 1.5\*the upper limit of the normal range (ULN); alanine aminotransferase and aspartate aminotransferase \<=2.5\*ULN. 3. Renal function: creatinine clearance \>=60 milliliter per minute (mL/min) either as estimated by the Cockcroft-Gault equation. 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)/magnetic resonance imaging (MRI) by local assessment. 2. Systemic anticancer treatment (including investigational agents) less than 3 weeks before the first dose of study treatment (\<=4 weeks for antibody-based therapy including unconjugated antibody, antibody-drug conjugate, and bi-specific T-cell engager agent; \<=8 weeks for cell-based therapy or anti-tumor vaccine). 3. Radiotherapy less than (\<) 3 weeks before the first dose of study treatment. If prior radiotherapy occurred \<4 to 6 weeks before the study start, as radiated lesions cannot be reliably assessed by fluoro-2-deoxy-D-glucose (FDG)-positron emission tomography (PET), nonradiated target lesions are required for eligibility. 4. Prior autologous stem cell transplant (ASCT) within 6 months or prior ASCT at any time without full hematopoietic recovery before Cycle 1 Day 1, or allogeneic stem cell transplant at any time. 5. Any clinically significant comorbidities, such as uncontrolled pulmonary disease (example, severe chronic obstructive pulmonary disease with hypoxemia, interstitial lung disease, radiation induced lung injury), known impaired cardiac function or clinically significant cardiac disease, active CNS disease, or any other condition that could, in the opinion of the investigator, compromise the participant's safety and participation in the study per protocol. 6. Known gastrointestinal (GI) disease or GI procedure that could interfere with the oral absorption or tolerance of TAK-659. 7. Use or consumption of any of the following substances: Received medications, supplements, or food/beverages that are P-glycoprotein (P-gp) inhibitors or inducers or strong cytochrome P450 (CYP) 3A inhibitors or inducers within a certain time frame prior to the first dose of study drug. Depending on the substance, the washout period for P-gp inhibitors or inducers or strong CYP3A inhibitors or inducers will be either 7 days or 5 times the half-life (half-life is related to the time required for elimination from the body). The washout period for grapefruit containing food or beverages is 5 days.