Gene Therapy in Treating Patients With Human Immunodeficiency Virus-Related Lymphoma Receiving Stem Cell Transplant

Inclusion Criteria * Inclusion criteria associated with type and status of lymphoma, one of the following must be applicable: * Biopsy-proven intermediate or high-grade non-Hodgkin's lymphoma, meeting one of the following criteria (timeline 8 months prior to enrollment in the screening segment): \- In partial remission, \- Relapsed after initial complete remission, \- Failed induction therapy, but responds to salvage therapy (i.e., chemosensitive disease), \- In complete remission with high-risk features as specified by the International Prognostic Index. * Biopsy-proven advanced stage follicular lymphoma, that have failed at least two lines of therapy multi-agent chemotherapy, but responds to salvage therapy i.e.,chemosensitive disease) (timeline 8 months prior to enrollment in the screening segment). * Biopsy-proven advanced stage Mantle cell lymphoma with Ki-67 \> 10% in first complete remission (timeline 8 months prior to enrollment in the screening segment). * Biopsy-proven Hodgkin's lymphoma, meeting one of the following criteria (timeline 8 months prior to enrollment). \- In first, or greater relapse after initial complete remission, \- In partial remission, \- Failed induction therapy, but responds to salvage therapy (i.e., chemosensitive disease). * Biopsy-proven Burkitt's lymphoma, meeting one of the following criteria (timeline 8 months prior to enrollment): \- In second complete remission after relapse following …