A Study of TAK-659 in Combination With NKTR-214 in Participants With Advanced Non-Hodgkin Lymphoma (NHL)

Inclusion Criteria: 1. Histologically or cytologically confirmed diagnosis of advanced B-cell NHL, including diffuse large B-cell lymphoma (DLBCL), follicular lymphoma (FL), marginal zone lymphoma (MZL), or mantle cell lymphoma (MCL) (Waldenstrom macroglobulinemia \[WM\] and chronic lymphocytic leukemia \[CLL\]/small lymphocytic leukemia \[SLL\] are excluded). 2. Radiographically or clinically measurable disease with at least 1 target lesion per (greater than \[\>\] 1.5 centimeter \[cm\] in the longest diameter for a lymph node or nodal mass, or \>1.0 cm in the longest diameter for extranodal disease) Lugano 2014 criteria for malignant lymphoma. 3. Participants who are refractory or relapsed after at least 2 prior lines of therapy due to progression, intolerance, or physician/participant decision, and for whom no effective standard therapy is available per the investigator's assessment. The sponsor may restrict prior lines of therapy in the expansion phase of the study based on emerging data. The decision may be documented and shared with investigators in a memo before the initiation of the dose expansion phase followed by updating the exclusion criteria in a subsequent amendment, if deemed necessary. Requirements for prior therapy depending on disease type are outlined in the protocol, however all patients must be ineligible for or have already failed hematopoietic stem cell transplant. 4. Eastern Cooperative Oncology Group (ECOG) performance status score of 0 or 1 and life expectancy of \>3 months. 5. Must have adequate organ function. 6. Recovered (that is, less than or equal to \[\<=\] Grade 1 toxicity) from the clinically significant 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. Exceptions include those participants who have completed definitive therapy, are not on steroids, have a stable neurologic status for at least 2 weeks after completion of the definitive therapy and steroids, and do not have neurologic dysfunction that would confound the evaluation of neurologic and other AEs. 2. Known human immunodeficiency virus (HIV) infection or HIV-related malignancy, hepatitis B surface antigen positive, or known or suspected active hepatitis C infection. 3. 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. 4. Systemic anticancer treatment (including investigational agents) or radiotherapy less than 2 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 agents; \<=8 weeks for cell-based therapy or antitumor vaccine). 5. Participants in need of immediate cytoreductive therapy. 6. Prior autologous stem cell transplant (ASCT) within 6 months or prior ASCT at any time without full hematopoietic recovery, defined by the entry criteria in the study, before Cycle 1 Day 1 or allogeneic stem cell transplant any time. 7. Use or consumption of: * Medications or supplements that are known to be inhibitors of P-glycoprotein (P-gp) and/or strong reversible inhibitors of cytochrome (CYP3A), strong CYP3A mechanism-based inhibitors, strong CYP3A inducers or P-gp inducers within 5 times the inhibitor half-life or within 7 days before the first dose of study drug. In general, the use of these agents is not permitted during the study except in cases in which an AE must be managed. * Grapefruit-containing food or beverages within 5 days before the first dose of study drug. Note that grapefruit-containing food and beverages are not permitted during the study. 8. Active, known, or suspected autoimmune disease. Participants requiring systemic treatment within the past 3 months or with a documented history of clinically severe autoimmune disease that requires systemic steroids or immunosuppressive agents. (Exceptions include any patient taking 10 mg or less of prednisone or equivalent, participants with vitiligo, hypothyroidism stable on hormone replacement, type 1 diabetes, Graves disease, Hashimoto disease, alopecia areata, eczema, or with medical monitor approval.) 9. History of organ or tissue transplant that requires systemic use of immunosuppressive agents. 10. Prior treatment with TAK-659 or any spleen tyrosine kinase (SYK) inhibitor or interleukin-2 (IL-2) therapy. 11. Use of \>2 antihypertensive medications for management of hypertension (including diuretics). 12. Major surgery within 14 days before the first dose of study drug and not recovered fully from any complications from surgery or systemic infection requiring intravenous antibiotic therapy or other serious infection within 14 days before the first dose of study drug. 13. Known gastrointestinal (GI) disease or GI procedure that could interfere with the oral absorption or tolerance of TAK-659, including difficulty swallowing tablets or diarrhea Grade \>1 despite supportive therapy. 14. Treatment with high-dose corticosteroids for anticancer purposes within 14 days before the first dose of TAK-659; daily dose equivalent to 10 mg oral prednisone or less is permitted.