Tacrolimus/Sirolimus/Methotrexate vs Tacrolimus/Methotrexate or Cyclosporine/Mycophenolate Mofetil for GVHD Prophylaxis After Reduced Intensity Allogeneic Stem Cell Transplantation for Patients With Lymphoma

Inclusion Criteria: * Patients will be eligible if their primary indication for transplantation is among the following: Indolent B-cell non-Hodgkin lymphoma (NHL); Aggressive B-Cell NHL; T-cell NHL; or Hodgkin Lymphoma. * Patients must have one of the following combinations of disease status and disease histology at the time of enrollment: 1) Patients may be transplanted as part of first-line therapy if they have one of the following histologies: CLL with adverse cytogenetics, MCL or, T-cell NHL. 2) Patients may be transplanted as part of treatment for relapsed or refractory disease without a prior autologous transplantation of they have one of the following histologies: Indolent NHL (including CLL/SLL), MCL or T-cell NHL. 3) Patients may be transplanted as part of treatment for disease that has relapsed or progressed after autologous transplantation if they have any of the histologies listed above. Patients may also be enrolled without a prior autologous transplantation if they have a contraindication to autologous transplantation, in the opinion of the treating clinician. 4) There is no minimal or maximal time interval from the patient's last anti-lymphoma therapy and the time of transplantation. * 18-72 years of age * Matched related or matched unrelated donor * Donor willing to donate peripheral blood stem cells and meeting institutional criteria for stem cell donation. The donor must be medically eligible to donate stem cells according to individual transplant center criteria. Exclusion Criteria: * Patients with Burkitt lymphoma or DLBCL with a c-myc rearrangement * Karnofsky performance status of less than 70% at the time of registration * Prior allogeneic stem cell transplantation (note that prior autologous stem cell transplantation is allowed) * Uncontrolled infection * Serum creatinine 2.0mg/dl or greater * Total bilirubin 2.0mg/dl or greater (unless related to hemolysis or Gilbert's syndrome) * Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) 3 times or greater than the institutional upper limit of normal * Left ventricular ejection fraction \< 30% * Cholesterol \> 500mg/dl or triglycerides \> 500 mg/dl despite appropriate treatment * Seropositivity for HIV * Pregnancy or breast-feeding (effective contraception must be used during therapy and for at least 6 months after the end of immunosuppressive agents) * Prior history of allergy to sirolimus, tacrolimus, cyclosporine, methotrexate or MMF * Concomitant treatment with another investigational drug (unless cleared by study chair)