Genetically Modified Peripheral Blood Stem Cell Transplant in Treating Patients With HIV-Associated Non-Hodgkin or Hodgkin Lymphoma

Inclusion Criteria: * HIV seropositive * Antiretroviral treatment for at least one month, defined as a multi-drug regimen (excluding azacitidine \[AZT\]) * HIV plasma viral load has decreased by 1.5 logs or viral load \< 5000 copies/ml * Non-Hodgkin or Hodgkin lymphoma without active central nervous system (CNS) involvement associated with poor prognosis with medical therapy alone or for which autologous peripheral blood stem cell (PBSC) transplant is indicated: * Hodgkin's lymphoma beyond first remission; first partial remission; induction failure with subsequent response to salvage therapy * Non-Hodgkin's Lymphoma beyond first remission: first partial remission; induction failure with subsequent response to salvage therapy * Chemotherapy responsive disease * Karnofsky performance score \>= 70% * Subjects must agree to use effective contraception from enrollment through completion of the study * Female subjects: if of child bearing potential, must have negative serum or urine pregnancy test within 7 days of treatment * Subjects must be on a prophylactic regimen for Pneumocystis carinii pneumonia, or agree to begin such treatment, if the cluster of differentiation (CD)4 counts are =\< 200 * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Serum creatinine \> 2 times upper limit of normal * Serum bilirubin greater than 3 times the upper limits of normal, unless determined to be a result of the primary hematol…