Safety and Efficacy of ALLO-501A Anti-CD19 Allogeneic CAR T Cells in Adults With Relapsed/Refractory Large B Cell Lymphoma, Chronic Lymphocytic Leukemia and Small Lymphocytic Lymphoma (ALPHA2)

Inclusion Criteria: For subjects with LBCL: * Histologically confirmed diagnosis of relapsed/refractory large B-cell lymphoma at last relapse per WHO 2017 * At least 1 measurable lesion at time of enrollment * Relapsed or refractory disease after at least 2 lines of chemotherapy * Absence of significant donor (product)-specific anti-HLA antibodies (DSA) at screening (Note: Only applicable for Phase 2) For subjects with CLL/SLL: * Diagnosis of CLL/SLL * Relapsed/refractory disease * Subjects relapsed/refractory to BTKi therapy and high-risk disease * Subjects relapsed/refractory with 2 or more lines of therapy including BTKi and BCL-2 inhibitor (venetoclax) * At least 1 measurable lesion at time of enrollment For all subjects: * Male or female subjects ≥18 years of age * Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0 or 1 * Adequate hematological, renal, and liver function Exclusion Criteria: * Active central nervous system (CNS) involvement by malignancy * Current thyroid disorder (including hyperthyroidism), except for subjects with hypothyroidism controlled on a stable dose of hormone replacement therapy * Any other active malignancies that required systemic treatment within 3 years prior to enrollment * Radiation therapy within 2 weeks prior to ALLO-647 * Prior irradiation to \>25% of the bone marrow * Hypocellular bone marrow for age by institutional standard as determined from a bone marrow biopsy performed at time of screening (Note: Only…