Inclusion Criteria:

          1. Must have histologically confirmed DLBCL, including de novo disease or transformed
             disease from indolent NHL.

             a. High-grade B-cell lymphoma (BCL) with MYC and BCL-2 and/or BCL-6 translocations
             (double-hit DLBCL under DLBCL, not otherwise specified [NOS], based on the 2008 World
             Health Organization [WHO] classification criteria) is not eligible for this study.

          2. Local pathology review for histological confirmation; A formalin-fixed,
             paraffin-embedded (FFPE) tumor block or appropriately stained slides from a fresh
             biopsy is required.

          3. Relapsed or refractory to greater than or equal to (>=) 2 prior lines of chemotherapy
             based on standard of care with certain requirements for prior therapy.

          4. Documented investigator-assessed relapse or progression after the last treatment is
             required if the participant responded and then progressed on the prior treatment.

          5. Measurable disease per IWG 2007 criteria.

          6. Eastern Cooperative Oncology Group (ECOG) performance status less than (<) 2.

          7. Life expectancy of greater than (>) 3 months.

          8. Adequate organ function, including the following:

               1. Bone marrow reserve: absolute neutrophil count (ANC) >=1000/microliter (μL),
                  platelet count >=75,000/μL (>=50,000/μL for participants with bone marrow
                  involvement), and hemoglobin >=8 gram per deciliter (g/dL).

               2. Hepatic: total bilirubin less than or equal to (<=) 1.5 times the upper limit of
                  the normal range (ULN); alanine aminotransferase (ALT) and aspartate
                  aminotransferase (AST) <=2.5*ULN.

               3. Renal: creatinine clearance >=60 milliliter per minute (mL/min).

               4. 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.

                    -  Glycosylated hemoglobin is <=6.5% hyperglycemic participants permitted if
                       glucose is well controlled by antihyperglycemic medication).

        Exclusion Criteria:

          1. Central nervous system (CNS) lymphoma; active brain or leptomeningeal metastases.

          2. Known human immunodeficiency virus (HIV)-related malignancy.

          3. 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 agents; <=8 weeks for cell-based therapy or anti-tumor vaccine).

          4. Radiotherapy less than 3 weeks before the first dose of study treatment. If prior
             radiotherapy occurred <4 to 6 weeks before study start, as radiated lesions cannot be
             reliably assessed by fluorodeoxyglucose-positron emission tomography (FDG-PET),
             nonradiated target lesions are required for eligibility, and prior radiotherapy
             information must be submitted to the IRC.

          5. Known HIV positive, hepatitis B surface antigen positive or known or suspected active
             hepatitis C infection.

          6. 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 any time.

          7. Participants with certain cardiovascular conditions are excluded.

          8. Major surgery within 14 days before the first dose of study drug or incomplete
             recovery from any complications from surgery.

          9. Systemic infection requiring parenteral antibiotic therapy or other serious infection
             (bacterial, fungal, or viral) within 21 days before the first dose of study drug.

         10. Treatment with high-dose corticosteroids for anticancer purposes within 7 days before
             the first dose of TAK-659.

         11. 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.

         12. Known gastrointestinal (GI) disease or GI procedure that could interfere with the oral
             absorption or tolerance of TAK-659.

         13. 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 timeframe 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.