This study focuses on individuals with large B-cell lymphoma who have completed initial therapy. The study aims to determine whether CAR T cells made from healthy donors are an effective treatment to prevent relapse in people who have lymphoma DNA detected in their blood by an experimental test. CAR T cells are T cells (a type of immune system white blood cell) that have been engineered to attack cancer cells such as lymphoma. The study evaluates 2 experimental products: ALLO-647, an antibody (protein) that may help prepare the body for receiving CAR T cells from healthy donors and cemacabtagene ansegedleucel (cema-cel), a CAR T cell study treatment. ALLO-647 decreases certain white blood cells in the body in preparation to receive cema-cel. ALLO-647 may be given as part of a combination of drugs aimed at temporarily decreasing the white blood cells in the body. Cema-cel is made in the laboratory by taking white blood cells from a healthy person (donor) and changing them so they target lymphoma cells. The donor’s T-cells are genetically modified (changes are made to the DNA or genes) to help them fight or kill cancer cells. The study also evaluates an experimental laboratory test on the blood that looks for DNA specific to the patient’s lymphoma. Participants will be randomly assigned to either continued observation (the current standard of care) without any experimental drug treatment, or study treatment with cema-cel. If randomly assigned to study treatment, the participant may or may not receive ALLO-647.