CD8+ Memory T-Cells as Consolidative Therapy After Donor Non-myeloablative Hematopoietic Cell Transplant in Treating Patients With Leukemia or Lymphoma

Participants undergo total lymphoid irradiation (TLI) on Days -11 to -7 and Days -4 to -1 and receive anti-thymocyte globulin (ATG) per standard institutional practice on Days -11 to -7. Patients also receive oral cyclosporine daily starting on Day -3, and will continue for at least 6 months post-transplant. Patients undergo standard non-myeloablative allogeneic HSCT on Day 0. Patients also receive oral mycophenolate mofetil daily beginning on Day 0 and continuing until Day 28. Participants receive an intravenous infusion of allogeneic cluster of differentiation 8 (CD8)+ memory T-cells over 10 to 20 minutes sometime between day 30 and day 60. PRIMARY OBJECTIVES: I. To determine the rate of conversion to full-donor chimerism (FDC) following a post-transplant infusion (Day 30-60) of freshly-enriched allogeneic CD8+ memory T-cells in patients with acute myeloid leukemia (AML), non-Hodgkin lymphoma (NHL), chronic lymphocytic leukemia (CLL), or Hodgkin lymphoma (HL), who received standard non-myeloablative total lymphoid irradiation (TLI) anti-thymocyte globulin (ATG) transplant conditioning. SECONDARY OBJECTIVES: I. To determine the risk of disease progression, overall and event free survival, and non-relapse mortality. II. To determine the incidence of acute and chronic graft-versus-host disease (GVHD) following the infusion of allogeneic CD8+ memory T-cells. OUTLINE: Patients undergo TLI on days -11 to -7 and -4 to -1 and receive ATG per standard institutional practice on days -11 to -7. Patients also receive cyclosporine orally (PO) daily starting on day -3 and will continue for at least 6 months post-transplant. Patients undergo non-myeloablative allogeneic hematopoietic stem cell transplant (HSCT) on day 0. Patients also receive mycophenolate mofetil PO daily beginning on day 0 and continue until day 28. Based on the patient's status after the initial transplant, patients receive CD8+ memory T-cells intravenously (IV) over 10-20 minutes sometime between day 30 and day 60. After completion of study treatment, patients are followed up periodically.