A Study of TAK-007 in Adults With Relapsed or Refractory (r/r) B-cell Non-Hodgkin Lymphoma (NHL)

Inclusion Criteria: 1. Participants who have a life expectancy ≥12 weeks. 2. Participants who have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 3. Participants with a diagnosis of previously treated r/r histologically proven Cluster of Differentiation (CD)19 expressing disease of the following types: a. LBCL, including the following subtypes defined by the World Health Organization (WHO): i. Diffuse large B-cell lymphoma (DLBCL) not otherwise specified (NOS). ii. High-grade B-cell lymphoma (HGBL) with MYC and BCL2 and/or BCL6 rearrangement iii. HGBL NOS without translocations. iv. DLBCL arising from iNHL including follicular lymphoma (FL) or marginal zone lymphoma (MZL). v. T-cell/histiocyte-rich LBCL. vi. DLBCL associated with chronic inflammation. vii. Epstein-Barr virus-positive DLBCL-NOS. viii. Primary cutaneous DLBCL, leg type. ix. Primary mediastinal large B-cell lymphoma (PMBCL). x. FL Grade 3B. b. iNHL, including the following subtypes defined by the WHO: i. FL Grades 1, 2, 3A. ii. MZL (nodal, extranodal, and splenic). 4. Participants who have measurable disease, defined as at least 1 lesion per the Lugano classification. Lesions situated in a previously irradiated area are considered measurable if radiographic progression has been documented in such lesions following completion of radiation therapy. LBCL should have positron emission tomography (PET) -positive disease per the Lugano classification. 5. Participants who have r/r LBCL or r/r iNHL after ≥2 prior lines of systemic therapy: (Expansion Cohorts 1A and 1B \[LBCL 3L+\], and 2A \[iNHL 3L +\]) or r/r LBCL after 1 prior line of systemic therapy (Expansion Cohort 1C \[LBCL 2L\]): 1. Participants with r/r LBCL must have received an anti-CD20 monoclonal antibody (mAb) and an anthracycline containing chemotherapy regimen and failed or be ineligible for high-dose chemotherapy and autologous stem cell transplantation (ASCT). 2. Participants with iNHL must have received an anti-CD20 mAb and an alkylating agent (eg, bendamustine or cyclophosphamide). 3. Preinduction salvage chemotherapy and ASCT should be considered 1 line of therapy. 4. 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. 5. Single-agent anti-CD20 mAb therapy should not be considered a line of therapy. 6. Bridging chemotherapy given just prior to CAR-T cell therapy treatment should be considered one line of therapy together with cell therapy. 7. Participants who have received prior CD19-targeting CAR-T cell therapy must have achieved at least a partial response to the most recent CD19-targeting CAR-T cell therapy. 8. Participants with 1 prior line of therapy in Part 1 Cohort 1C must have either: * refractory disease to first-line chemoimmunotherapy or relapse within 12 months of first-line chemoimmunotherapy OR * relapsed or refractory disease and be ineligible for intensive chemoimmunotherapy and/or high-dose chemotherapy followed by ASCT due to comorbidities and/or age. 6. Participants who have adequate bone marrow function defined as follows: 1. Absolute neutrophil count \>500/μL. 2. Platelet count of \>50,000/μL at screening. Participants with transfusion-dependent thrombocytopenia are excluded. 7. Participants who have adequate renal, hepatic, cardiac, and pulmonary function as defined in the study protocol: 1. Estimated glomerular filtration rate (GFR; Modification of Diet in Renal Disease equation \[MDRD\]) ≥30 mL/min. 2. Serum alanine aminotransferase/aspartate aminotransferase ≤5 times the upper limit of normal range (ULN), as long as participant is asymptomatic. 3. Total bilirubin ≤2 mg/dL. Participants with Gilbert's syndrome may have a bilirubin level \>2 × ULN, per discussion between the investigator and the medical monitor. 4. Left ventricular ejection fraction (LVEF) ≥40% as determined by an echocardiogram (ECHO) or multigated acquisition (MUGA) scan performed within 1 month of determination of eligibility. 5. No evidence of clinically relevant pericardial effusion, and no acute clinically significant electrocardiogram (ECG) findings. 6. Absence of Grade ≥2 pleural effusion. Grade 1 stable pleural effusions are allowed. 7. Baseline oxygen saturation \>92% on room air. 8. Participants are required to consent to provide either sufficient archived formalin-fixed paraffin embedded (at least 10 unstained slides, ideally 20 unstained slides) or fresh tumor tissue obtained after the last relapse (see laboratory manual for details). Exception may be granted by sponsor medical monitor per discussion with investigator. Exclusion Criteria: 1. Participants with total body weight of \<40 kg. 2. Participants with primary or secondary central nervous system (CNS) involvement by lymphoma. Participants with a history of secondary CNS involvement by lymphoma without evidence of CNS involvement at screening may be included. 3. Participants with Burkitt lymphoma, mantle cell lymphoma, lymphoplasmocytic lymphoma, or transformation from CLL/small lymphocytic lymphoma (Richter transformation). 4. Participants with a history of malignancy other than nonmelanoma skin cancer, carcinoma in situ (eg, cervix, bladder, breast), low-grade tumors deemed to be cured and not treated with systemic therapy (eg, by gastro-endoscopy curatively removed gastric cancer) or unless disease free for ≥3 years at screening. 5. Participants who have undergone autologous or allogeneic transplant or Chimeric antigen receptor T cells (CAR-T) or Chimeric antigen receptor Natural Killer cells (CAR-NK) therapy within 3 months of planned enrollment. Participants after allogeneic transplant have to be off systemic immunosuppressive therapy and without the evidence of clinically relevant acute or chronic graft-versus-host disease (GvHD) at the time of enrollment. 6. Treatment with any investigational products or any systemic anticancer treatment within 14 days or 2 half-lives of the treatment (whichever is longer) before conditioning therapy. For rituximab, a half-life of 22 days should be considered. 7. Participants with active infection, including fungal, bacterial, viral, or other infection that is uncontrolled or requires IV antimicrobials for management within 3 days before enrollment. 8. Participants with a history or presence of active or clinically relevant CNS disorder, such as seizure, encephalopathy, cerebrovascular ischemia/hemorrhage, severe dementia, cerebellar disease, or any autoimmune disease with CNS involvement. For CNS disorders that recover or are in remission, participants without recurrence within 2 years of planned study enrollment may be included. 9. Participants with any of the following within 6 months of enrollment: myocardial infarction, cardiac angioplasty or stenting, unstable angina, symptomatic congestive heart failure (ie, New York Heart Association Class II or greater), clinically significant arrythmia (including uncontrolled atrial fibrillation), or any other clinically significant cardiac disease. 10. Participants who have received a live vaccine ≤6 weeks before the start of the conditioning regime.