This is a single-arm, open label, multicenter Phase 1/2 study evaluating ALLO-501A in adult subjects with R/R LBCL and CLL/SLL. The purpose of the ALPHA2 study is to assess the safety, efficacy, and cell kinetics of ALLO-501A in adults with relapsed or refractory large B-cell lymphoma and assess the safety of ALLO-501A in adults with relapsed or refractory chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL) after a lymphodepletion regimen comprising fludarabine, cyclophosphamide, and ALLO-647.