This is a phase 1 study of FT522 administered with rituximab in participants with relapsed/refractory B-cell lymphoma (R/R BCL). The primary objectives of the study are to evaluate the safety and tolerability of FT522 in combination with rituximab, and to determine the recommended phase 2 dose (RP2D) of FT522 in combination with rituximab; each objective will be assessed with or without conditioning chemotherapy.

Inclusion Criteria:

• Diagnosis of B-cell lymphoma (BCL) as: (1) histologically documented lymphomas expected to express CD19 and CD20, including Grades 1 to 3B follicular lymphoma (FL), marginal zone lymphoma (MZL), Waldenstrom macroglobulinemia (WM), mantle cell lymphoma (MCL), transformed indolent non-Hodgkin lymphoma (tNHL), diffuse large B-cell lymphoma (DLBCL) [not otherwise specified], high-grade BCL, primary mediastinal BCL, and Richter transformation (RT; expansion part of study only); (2) R/R disease following at least 1 prior systemic regimen containing an anti-CD20 monoclonal antibody (mAb) for which the participant has no available curative treatment options; and (3) evaluable F-fluorodeoxyglucose (FDG)-avid disease, or measurable disease defined by at least one bi dimensionally measurable lesion
• Male participants and female participants of childbearing potential who engage in heterosexual intercourse must agree to use protocol-specified method(s) of contraception

Exclusion Criteria:

• Females who are pregnant or breastfeeding
• Eastern Cooperative Oncology Group (ECOG) Performance Status ≥2
• Body weight <50 kg
• Evidence of insufficient organ function
• Receipt of any biological therapy, chemotherapy (except for rituximab), or any investigational therapy within 2 weeks prior to Day 1 or five half-lives, whichever is shorter; or localized radiation therapy to a target lesion within 14 days prior to Day 1
• Currently receiving or likely to require systemic immunosuppressive therapy, e.g., prednisone >5 mg daily, for any reason from Day -5 to Day 29, with the exception of corticosteroids as a pre medication required for conditioning chemotherapy or rituximab
• Prior allogeneic hematopoietic stem cell transplant (HSCT) or allogeneic chimeric antigen receptor (CAR) T-cell therapy within 6 months of Day 1, or ongoing requirement for systemic graft-versus-host disease (GvHD) therapy
• Receipt of an allograft organ transplant
• Non-malignant central nervous system (CNS) disease such as stroke, epilepsy, CNS vasculitis, or neurodegenerative disease or receipt of medications for these conditions in the 2-year period leading up to study enrollment
• Clinically significant cardiovascular disease
• Clinically significant infections
• Receipt of a live vaccine <6 weeks prior to start of study intervention
• Known allergy to human albumin or DMSO
• Any medical condition or clinical laboratory abnormality that per investigator or medical monitor judgement, precludes safe participation in and completion of the study, or that could affect compliance with protocol conduct or interpretation of results

The initial dose escalation stage of the study is nonrandomized; the dose optimization stage is randomized; the dose expansion stage is nonrandomized.