This study looks at the use of a special treatment called ALLO-501A for adults with certain blood cancers, like large B-cell lymphoma (LBCL), chronic lymphocytic leukemia (CLL), and small lymphocytic lymphoma (SLL). ALLO-501A is a type of CAR T-cell therapy, where T-cells (a type of white blood cell) are changed in a lab to fight cancer more effectively. The study checks if this treatment is safe and effective for people whose cancer has come back or didn’t respond to other treatments.

Participants will receive a treatment to prepare their body called a lymphodepletion regimen, which includes medicines like fludarabine, cyclophosphamide, and ALLO-647.

• The study is open to adults aged 18 or older with certain types of lymphoma or leukemia.
• Participants must have tried at least two other treatments before.
• They must be able to visit the study center for assessments and treatment.

Before joining, participants will be checked to meet all the necessary conditions and must not have certain health issues, like active brain cancer or thyroid problems. The study aims to find out if ALLO-501A can help those whose cancer did not improve with other treatments.