A Study of TAK-659 in Combination With Bendamustine (+/-Rituximab), Gemcitabine, Lenalidomide, or Ibrutinib for the Treatment of Participants With Advanced Non-Hodgkin Lymphoma

Inclusion Criteria:

1. Male or female participants aged 18 years or older.
2. In the dose escalation phase, histologically or cytologically confirmed diagnosis of advanced non-Hodgkin lymphoma (NHL) of any histology (with the exception of participants with Waldenström macroglobulinemia \[WM\] and chronic lymphocytic leukemia \[CLL\]). In the safety expansion phase for Cohort B, only participants with advanced FL or MZL will be included.
3. Radiographically or clinically measurable disease with at least 1 target lesion per International Working Group (IWG) criteria for malignant lymphoma.
4. In the dose escalation phase, participants who are refractory or relapsed after at least 1 prior line of therapy due to progression, intolerance, or physician/participant decision and for whom no effective standard therapy is available per the investigator's assessment. In the safety expansion phase for Cohort B in participants with FL or MZL, the prior line of therapy is limited to \<=1.

   * Either treatment naive to, relapsed/refractory to, or experienced treatment failure due to other reasons with ibrutinib, idelalisib, or any other investigational B-cell receptor (BCR) pathway inhibitors not directly targeting spleen tyrosine kinase (SYK).
   * Pre induction salvage chemotherapy and autologous stem cell transplant (ASCT) should be considered 1 therapy.
   * Any consolidation/maintenance therapy after a chemotherapy regimen (without intervening relapse) should be considered 1 line of therapy with the preceding combination therapy. Maintenance antibody therapy should not be considered a line of therapy.
   * For aggressive NHL (i.e., diffuse large B-cell lymphoma \[DLBCL\]), single-agent anti-CD20 monoclonal antibody therapy should not be considered a line of therapy. Antibody therapy in participants with indolent NHL (i.e., FL) given as a single agent after disease progression from a prior treatment should be considered a line of therapy.
   * For participants with DLBCL transformed from indolent lymphoma, any treatment received for the indolent disease before the transformation to DLBCL will, in general, not count toward the 2 to 3 prior lines of therapy required for DLBCL in this study.
   * Prior treatment with a regimen that includes the combination drug will not necessarily exclude a participant from that cohort if the investigator views treatment with that agent as appropriate. However, a participant who has a contraindication for a particular combination agent or who has been discontinued from prior therapy with a particular agent for toxicity will not be eligible for inclusion in that particular cohort.
5. Eastern Cooperative Oncology Group (ECOG) performance status score of 0 or 1 and life expectancy of greater than 3 months.
6. Participants must have adequate organ function, including the following:

   * Adequate bone marrow reserve: absolute neutrophil count (ANC) greater than or equal to (\>=) 1000 per micro liter (/mcL), platelet count \>=75,000/mcL (\>=50,000/mcL 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).
   * Hepatic: total bilirubin less than or equal to (\<=) 1.5×the upper limit of the normal range (ULN); alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \<=2.5×ULN.
   * Renal: serum creatinine \>=60 milliliter per minute (mL/min) as estimated by the Cockcroft-Gault equation.
   * Others

     * Lipase \<=1.5×ULN and amylase \<=1.5×ULN with no clinical symptoms suggestive of pancreatitis or cholecystitis.
     * Blood pressure \<=Grade 1 (hypertensive participants are permitted if their blood pressure is controlled to \<= Grade 1 by hypertensive medications and glycosylated hemoglobin is \<=6.5%).
     * Fasting serum glucose level shall be controlled to 130 milligrams per deciliter (mg/dL) during the screening period.
7. Female participants who:

   * Are postmenopausal for at least 1 year before the screening visit, or
   * Are surgically sterile, or
   * If they are of childbearing potential, agree to practice 1 highly effective method of contraception and 1 additional effective (barrier) method at the same time, from the time of signing the informed consent through 180 days after the last dose of study drug, or
   * Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the participant. (Periodic abstinence \[example, calendar, ovulation, symptothermal, postovulation methods\] withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception. Female and male condoms should not be used together.)

   Male participant, even if surgically sterilized (that is, status postvasectomy), who:
   * Agree to practice effective barrier contraception during the entire study treatment period and through 180 days after the last dose of study drug, or
   * Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the participant. (Periodic abstinence \[example, calendar, ovulation, symptothermal, postovulation methods\], withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception. Female and male condoms should not be used together.)
   * Women of childbearing potential (WOCBP) must have a negative serum pregnancy test (minimum sensitivity 25 international units per liter IU/L or equivalent units of human chorionic gonadotropin \[hCG\]) at screening.
8. Both men and women in the rituximab combination arm (Cohort B) must practice contraception as described above from the time of signing of the informed consent form (ICF) through 12 months after the last dose of study drug.
9. Female participants should not donate ova from the time of signing the informed consent through 180 days after the last dose of study drug.
10. Male participants should not donate sperm from the time of signing the informed consent through 180 days after the last dose of study drug.
11. Both men and women in the lenalidomide combination arm (Cohort D) must adhere to the guidelines of the RevAssist program (United States participants) or, if not using commercial supplies, must adhere to the Lenalidomide Pregnancy Risk Minimisation Plan as outlined in the Study Manual.
12. Both men and women in the lenalidomide combination arm (Cohort D) must adhere to the guidelines of the RevAssist program (United States participants) or, if not using commercial supplies, must adhere to the Lenalidomide Pregnancy Risk Minimisation Plan as outlined in the Study Manual.
13. Voluntary written consent must be given before performance of any study-related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the participant at any time without prejudice to future medical care.
14. Recovered (that is, \<= 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). 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 adverse events (AEs).
2. Known human immunodeficiency virus (HIV)-related malignancy.
3. Known hypersensitivity (example, anaphylactic and anaphylactoid reactions) to any particular combination drug will result in a participant being ineligible for inclusion in that particular cohort.
4. For participant in the lenalidomide combination arm, demonstrated hypersensitivity (example, angioedema, Stevens-Johnson syndrome, toxic epidermal necrolysis) to lenalidomide.
5. History of drug-induced pneumonitis requiring treatment with steroids; history of idiopathic pulmonary fibrosis, organizing pneumonia, or evidence of active pneumonitis on screening chest computerized tomography (CT) scan; history of radiation pneumonitis in the radiation field (fibrosis) is permitted.
6. Life-threatening illness unrelated to cancer that could, in the investigator's opinion, make the participant not appropriate for this study.
7. Female participants who are lactating and breast-feeding or a positive serum pregnancy test during the Screening period or a positive urine pregnancy test on Day 1 before the first dose of study drug.
8. Any serious medical or psychiatric illness, including drug or alcohol abuse, that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol.
9. Known human immunodeficiency virus (HIV) positive.
10. Known hepatitis B surface antigen positive, or known or suspected active hepatitis C infection.
11. Systemic anticancer treatment (including investigational agents) or radiotherapy less than 2 weeks before the first dose of study treatment (\<=4 weeks 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).
12. Prior ASCT within 6 months or prior ASCT at any time without adequate full hematopoietic recovery, defined by the entry criteria in the study, before Cycle 1 Day 1 or allogeneic stem cell transplant any time.
13. Any clinically significant comorbidities, such as uncontrolled pulmonary disease, known impaired cardiac function or clinically significant cardiac disease (specified below), active central nervous system (CNS) disease, active infection, or any other condition that could compromise the participant's participation in the study.
14. Participants with any of the following cardiovascular conditions are excluded:

    * Unstable angina or acute myocardial infarction within 12 months before starting study drug.
    * Current or history of New York Heart Association Class III or IV heart failure.
    * Evidence of current, uncontrolled cardiovascular conditions including cardiac arrhythmias, angina, pulmonary hypertension, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities.
    * Friderichia corrected QT interval (QTcF) \>450 milliseconds (msec) (men) or \>475 msec (women) on a 12-lead electrocardiogram (ECG) during the Screening period.
    * Abnormalities on 12-lead ECG including, but not limited to, changes in rhythm and intervals that, in the opinion of the investigator, are considered to be clinically significant.
15. Lack of suitable venous access for the study-required blood sampling for TAK-659.
16. For participants in all combination arms (Cohorts A-E), use or consumption of any of the following substances:

    * Medications or supplements that are known to be inhibitors of P-glycoprotein (P-gp) and/or strong reversible inhibitors of cytochrome P450 (CYP) 3A within 5 times the inhibitor half-life (if a reasonable half-life estimate is known) or within 7 days (if a reasonable half-life estimate is unknown) 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. See a nonexhaustive list of prohibited strong CYP3A reversible inhibitors and/or P-gp inhibitors based on the US Food and Drug Administration (FDA) Draft Drug-Drug Interactions (DDI) Guidance.
    * Medications or supplements that are known to be strong CYP3A mechanism-based inhibitors or strong CYP3A inducers and/or P-gp inducers within 7 days or within 5 times the inhibitor or inducer half-life (whichever is longer) before the first dose of study drug. The use of these agents is not permitted during the study. See a list of prohibited strong CYP3A mechanism-based inhibitors or strong CYP3A inducers and/or P-glycoprotein (gp) inducers based on the United States (US) Food and Drug Administration (FDA) Draft Drug-drug Interaction (DDI) Guidance.
    * 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.
17. Additionally, for participants in the ibrutinib combination arm (Cohort E), use or consumption of any of the following substances:

    * Medications or supplements that are known to be moderate reversible inhibitors of CYP3A within 5 times the inhibitor half-life (if a reasonable half-life estimate is known) or within 7 days (if a reasonable half-life estimate is unknown) before the first dose of study drugs. In general, the use of these agents is not permitted during the study for this combination except in cases in which an adverse event (AE) must be managed. See a list of nonexhaustive moderate CYP3A reversible inhibitors based on the US FDA Draft DDI Guidance.
    * Medications or supplements that are known to be moderate mechanism-based inhibitors or moderate inducers of CYP3A 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 for this combination except in cases in which an AE must be managed. See a list of non-exhaustive moderate CYP3A mechanism-based inhibitors or moderate CYP3A inducers based on the US FDA Draft DDI Guidance.
    * Seville oranges within 5 days before the first dose of study drugs and during the study.
18. Major surgery within 14 days before the first dose of study drug and not recovered fully from any complications from surgery.
19. Systemic infection requiring intravenous (IV) antibiotic therapy or other serious infection within 14 days before the first dose of study drug.
20. Participants with another malignancy within 2 years of study start. Participants with nonmelanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone complete resection and are considered disease-free at the time of study entry.
21. 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.
22. 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. Corticosteroids for topical use or in nasal spray or inhalers are allowed.