Allogeneic Hematopoietic Stem Cell Transplantation Using a Non-myeloablative Preparative Regimen of Total Lymphoid Irradiation and Anti-thymocyte Globulin for Older Patients With Relapsed Lymphoid Malignancies

Inclusion Criteria: * Any patient with one of the following hemato-lymphoid malignancies or syndromes in whom allogeneic stem cell transplantation is warranted. Specific disease categories include: non-follicular indolent advanced stage Non-Hodgkin Lymphomas, Mantle Cell Lymphoma, Marginal zone lymphoma, MALT, T cell lymphoma, Chronic Lymphocytic or prolymphocytic Leukemia, Hodgkin Disease, and Waldenström macroglobulinemia. T-cell NOS, angioimmunoblastic lymphoma, HTLV1, T-gamma/delta, anaplastic lymphoma and Sezeay syndromes can be included after careful assessment by the PI and the protocol steering committee. * Patients must be at least in partial remission (according to standard criteria) after salvage therapy and before (\~one month) the start of the conditioning regimen. * Patient age \>50 and less than 66 years, or for patients \<50 years of age but because of pre-existing medical conditions or prior therapy are considered to be at high risk for regimen-related toxicity associated with conventional myeloablative transplants. * A fully HLA-identical sibling or matched unrelated donor is available (10/10 HLA match). Patients with one antigen mismatched donors can be considered but only after discussion with the transplant team and the Principal Investigator. * Patient must be competent to give consent. Exclusion Criteria: * Patients with progressive hematolymphoid malignancies despite conventional therapies, and not in partial remission during the month preceding transplantation. * Patients with DLBCL or cutaneous T cell lymphoma * Uncontrolled CNS involvement with disease * Fertile men or women unwilling to use contraceptive techniques during and for 12 months following treatment * Females who are pregnant * Organ dysfunction defined as follows: * Cardiac function: ejection fraction \<30% or uncontrolled cardiac failure * Pulmonary: DLCO \<40% predicted * Renal: Serum creatinine \>1.0 mg/dL; if serum creatinine \>1.0 mg/dL, then the estimated glomerular filtration rate (GFR) must be \>60 mL/min/1.73 m² * Liver function abnormalities: elevation of bilirubin to \> 3 mg/dl and/or transaminases \>4x the upper limit of normal * Karnofsky performance score \< 70% * Patients with poorly controlled hypertension on multiple antihypertensives * Documented fungal disease that is progressive despite treatment * Viral infections: HIV positive patients. Hepatitis B and C positive patients will be evaluated on a case by case basis * Psychiatric disorders or psychosocial problems which in the opinion of the primary physician or Principal Investigator would place the patient at unacceptable risk from this regimen. * Patients with prior malignancies diagnosed \> 5 years ago without evidence of disease are eligible. Patients with a prior malignancy treated \< 5 years ago but have a life expectancy of \> 5 years for that malignancy are eligible.