Reduced-Intensity Regimen Before Allogeneic Transplant for Patients With Relapsed Non-Hodgkin's or Hodgkin's Lymphoma

Inclusion Criteria: * Non-Hodgkin's or Hodgkin's lymphoma that has relapsed following either a course of high dose chemotherapy or autologous stem cell transplantation. * \>= 90 days from prior transplant. * Have a suitable human leukocyte antigen (HLA)-matched related bone marrow donor or a compatible matched unrelated bone marrow donor by molecular typing at HLA A, B, C, D, DR. * Physically and psychologically capable of undergoing bone marrow transplantation and its attendant period of strict isolation. * Age \>= 18 years * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Be able to receive 400 cGy Total Body Irradiation (TBI). * Pulmonary function tests: Diffusing capacity or Transfer factor of the lung for carbon monoxide (DLCO) \>= 50% predicted, the forced expiratory volume in 1 second (FEV1) \>= 50% predicted. * Left ventricular ejection fraction (LVEF) at least 45% by Multi Gated Acquisition Scan (MUGA) or echocardiogram. * Renal function: creatinine clearance \> 50 ml/min. * Liver function tests: \< 3 x Upper Limit of Normal (ULN). Liver function test include serum glutamic oxaloacetic transaminase (SGOT) (Aspartate transaminase (AST)), Serum Glutamic Pyruvate Transaminase (SGPT) (Alanine transaminase (ALT)), and bilirubin. Exclusion Criteria: * Human immunodeficiency virus positive (HIV+) patients (test positive for P21 antibodies to HIV). * Evidence of active infection (have received parenteral antibiotics \<= 2 weeks prior to registration). *…