This study is for adults with types of blood cancer called large B-cell lymphoma (LBCL) and chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL) that have come back or are not responding to treatment. The study is testing a new treatment called ALLO-501A, which is a type of therapy using special cells called CAR T cells. CAR T cells are cells taken from the immune system and changed to better fight cancer. Participants will first get medicines (fludarabine, cyclophosphamide, and ALLO-647) to help prepare their body for the CAR T cells. This study will check how safe and effective ALLO-501A is.

• The study requires multiple visits to the research center.
• Participants must be 18 years or older and have tried at least two other treatments.
• Some people may not qualify if they have other active cancers or certain health conditions.