This study is an open-label, multicenter, phase 1, dose escalation study of TAK-659 in adult participants with advanced solid tumor and lymphoma malignancies. This study will be the first to administer TAK-659 to humans. The participants population during dose escalation (Part A) will consist of adults previously diagnosed with any form of a solid tumor or lymphoma for which standard, curative, or life-prolonging treatment does not exist or is no longer effective. This first-in-human (FIH) study will include 5 dose expansion cohorts in refractory and/or relapsed Chronic Lymphocytic Leukemia (CLL), Diffuse Large B Cell Lymphoma (DLBCL), indolent Non Hodgkin Lymphoma (iNHL), Mantle Cell Lymphoma (MCL), Post Transplant Lymphoproliferative Disorder (PTLD) (Part B) following completion of dose escalation (Part A).

Inclusion Criteria:

Each participant must meet all of the following inclusion criteria to be enrolled in the study:

1. Male or female participants 18 years or older.

2. To be enrolled to the dose escalation (Part A), participants must have

   1. histologically or cytologically confirmed diagnosis of metastatic and/or advanced solid tumor malignancy or lymphoma, for which no effective standard treatment is available. However, participants with primary brain tumors or WM will be excluded.
   2. Radiographically or clinically measurable or nonmeasurable (but evaluable) disease. Radiographically measurable disease is determined by RECIST (version 1.1) for solid tumors or by International Working Group (IWG) criteria for malignant lymphoma (2007 IWG).

3. To be enrolled to the dose expansion cohorts (Part B), participants must meet the following criteria:

   1. Diagnosis of CLL that meets International Workshop on Chronic Lymphocytic Leukemia (IWCLL) 2008 criteria for Cohort 1; pathologically confirmed diagnosis of DLBCL for Cohort 2; histologically confirmed diagnosis of B-cell NHL (follicular lymphoma [FL] [Grade 1, 2, or 3a], small lymphocytic lymphoma (SLL), lymphoplasmacytoid lymphoma/Waldenström macroglobulinemia (LPL/WM), marginal zone lymphoma (MZL) [splenic, nodal, or extra-nodal]) for Cohort 3; histologically confirmed diagnosis of MCL for Cohort 4; and histologically confirmed diagnosis of PTLD (early lesion, polymorphic, monomorphic, classical Hodgkin lymphoma-type, Epstein-Barr virus (EBV) -positive DLBCL of the elderly, DLBCL associated with chronic inflammation; along with documented or documentable Epstein-Barr virus-encoded small RNA (EBER) status by tissue in situ hybridization [ISH]) for Cohort 5; histologically confirmed DLBCL (de novo or transformed disease from iNHL) for Cohort 6.
   2. Must have received greater than or equal to (>=) 1 prior therapy (excluding radiation); documented PD (MCL); either treatment naïve to, relapsed/refractory to, or treatment failure due to other reasons with ibrutinib, idelalisib, or any other investigational B-cell receptor (BCR) in pathway inhibitors not directly targeting Spleen tyrosine kinase (SYK); considered not appropriate for treatment or retreatment with purine analog-based therapy (CLL); or considered ineligible for at least 1 prior therapy (PTLD); or relapsed or refractory to >= 2 prior lines of chemotherapy (including standard first line therapy including Rituximab and an anthracycline [or equivalent if contraindicated] and one additional systemic multiagent chemotherapy as second-line salvage therapy that may have included autologous stem cell transplant (ASCT) [unless ineligible for salvage therapy and ASCT]) and should not have failed more than 4 prior lines of therapy (DLBCL Cohort 6).
   3. Radiographically or clinically measurable and/or evaluable disease as specified in the protocol.

4. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1.

5. Participants must have adequate organ function, including bone marrow reserve, hepatic, renal, pancreatic function and controlled blood pressure as described in the protocol.

6. Female participants who are postmenopausal for at least 1 year, are surgically sterile, or if of childbearing potential who agree to use 2 effective method(s) of contraception during the study treatment period through 6 months after the last dose of study drug or practice true abstinence.

   Male participants, even if surgically sterilized, who agree to practice effective barrier contraception during the study treatment period through 6 months after the last dose of study drug or practice true abstinence.

7. 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.

8. Participants must have recovered from the reversible effects of prior anticancer therapy (to Grade less than or equal to (<=) 1).

Exclusion Criteria:

Participants meeting any of the following exclusion criteria are not to be enrolled in the study.

1. Participants with brain metastasis, or participants with central nervous system (CNS) lymphoma or participants with another malignancy within two years of study start, with exceptions as described in the protocol.
2. 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.
3. Life-threatening illness unrelated to cancer; major surgery within 14 days before the first dose of study drug; systemic infection requiring intravenous (IV) antibiotic therapy or other serious infection (bacterial, fungal, or viral) within 21 days before the first dose of study drug.
4. Female participants who are pregnant or lactating.
5. Any immunotherapy, chemotherapy, radiotherapy, or investigational therapy within 3-4 weeks before the first dose of study treatment, as detailed in the protocol.
6. For escalation cohort or expansion cohorts excluding PTLD, ASCT within 6 months before Day 1 of Cycle 1, or prior ASCT at any time without full hematopoietic recovery before Day 1 of Cycle 1, or prior allogeneic stem cell transplant at any time.
7. Treatment with high dose corticosteroids (> daily dose equivalent to 10 milligram (mg) oral prednisone) for anticancer purposes within 7 days before the first dose of TAK-659.
8. Known human immunodeficiency virus (HIV) positive; known hepatitis B surface antigen-positive; or known or suspected active hepatitis C infection (testing not required).
9. Evidence of currently uncontrolled cardiovascular conditions as listed in the protocol.
10. Known gastrointestinal (GI) disease or GI procedure that could interfere with the oral absorption or tolerance of TAK-659 including difficulty swallowing tablets; diarrhea > Grade 1 despite supportive therapy.
11. Lack of suitable venous access for required blood sampling.
12. Use or consumption of P-glycoprotein (P-gp) inducers/inhibitors and/or strong CYP3A inducers/inhibitors as described in the protocol, and grapefruit-containing food or beverages as described in the protocol.

Takeda makes patient-level, de-identified data sets and associated documents available after applicable marketing approvals and commercial availability have been received, an opportunity for the primary publication of the research has been allowed, and other criteria have been met as set forth in Takeda's Data Sharing Policy (see www.TakedaClinicalTrials.com/Approach for details). To obtain access, researchers must submit a legitimate academic research proposal for adjudication by an independent review panel, who will review the scientific merit of the research and the requestor's qualifications and conflict of interest that can result in potential bias. Once approved, qualified researchers who sign a data sharing agreement are provided access to these data in a secure research environment.