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

The product being tested in this study is called TAK-007. TAK-007 is being tested to evaluate the safety and tolerability in adult participants with r/r B-cell NHL. The study will include 2 parts: Part 1 (Dose escalation and dose expansion) and Part 2. In Part 1, dose escalation cohorts' participants will receive TAK-007 as follows: Part 1 dose escalation: * Part 1: Dose escalation: TAK-007 - 200×10\^6 CD19-CAR+ Viable NK (Natural Killer) Cells (±30%) * Part 1: Dose escalation: TAK-007 - 800×10\^6 CD19-CAR+ Viable NK Cells (±25%) In Part 1 dose expansion phase, separate expansion cohorts for LBCL and iNHL (Cohorts 1A \[LBCL 3L+\] and 2A \[iNHL 3L+\]) and two additional dose expansion cohorts with a multi-dose regimen will be added (i.e., Cohort 1B and 1C) to evaluate more than 1 doses of TAK-007 after a 3-day regimen of lymphodepleting chemotherapy. Part 1 dose expansion cohorts' participants will receive TAK-007 as follows: * Part 1: Dose expansion: Cohort 1 (LBCL 3L+): TAK-007 - 800×10\^6 CD19-CAR+ Viable NK Cells on Day 0 of the study. * Part 1: Dose expansion: Cohort 2 (iNHL 3L+): TAK-007 - 800×10\^6 CD19-CAR+ Viable NK Cells on Day 0 of the study. Based on the data in Part 1, a single TAK-007 dose level will be selected by the sponsor and investigators as the recommended phase 2 dose (RP2D). Once RP2D is determined, participants will be enrolled in Part 2 of the study in the following cohorts: * Cohort 1: TAK-007 (LBCL) * Cohort 2: TAK-007 (iNHL) This multi-center trial will be conducted worldwide. Part 1 of the study will be conducted in the US, and Part 2 will be conducted worldwide. The overall time to participate in this study is 5 years. Participants will make multiple visits to the clinic and will enroll in a separate, long-term, follow-up study for continued safety assessments for up to 15 years after TAK-007 administration.