FT596 as a Monotherapy and in Combination With Anti-CD20 Monoclonal Antibodies

Key Inclusion Criteria: Diagnosis of B-cell lymphoma or CLL as described below: B-Cell Lymphoma: * Histologically documented lymphomas expected to express CD19 and CD20 * Relapsed/refractory disease following prior systemic immunochemotherapy regimen Chronic Lymphocytic Leukemia (CLL): * Diagnosis of CLL per iwCLL guidelines * Relapsed/refractory disease following at least two prior systemic treatment regimens ALL SUBJECTS: * Capable of giving signed informed consent * Age ≥ 18 years old * Stated willingness to comply with study procedures and duration * Contraceptive use for women and men as defined in the protocol Key Exclusion Criteria: ALL SUBJECTS: * Females who are pregnant or breastfeeding * Eastern Cooperative Oncology Group (ECOG) Performance Status ≥2 * Body weight \<50 kg * Evidence of insufficient organ function * Receipt therapy within 2 weeks prior to Day 1 or five half-lives, whichever is shorter; or any investigational therapy within 28 days prior to Day 1 * Currently receiving or likely to require systemic immunosuppressive therapy * Prior allogeneic hematopoietic stem cell transplant (HSCT) or allogeneic CAR-T within 6 months of Day 1, or ongoing requirement for systemic GvHD therapy * Receipt of an allograft organ transplant * Known active central nervous system (CNS) involvement by malignancy * Non-malignant CNS disease such as stroke, epilepsy, CNS vasculitis, or neurodegenerative disease * Clinically significant cardiovascular disease * Known HIV infection * Known active Hepatitis B (HBV) or Hepatitis C (HCV) infection * Live vaccine \<6 weeks prior to start of lympho-conditioning * Known allergy to albumin (human) or DMSO