Gene Therapy-Treated Stem Cells in Treating Patients Undergoing Stem Cell Transplant for Intermediate-Grade or High-Grade AIDS-Related Lymphoma

Inclusion Criteria: * HIV seropositive at or before the time of lymphoma diagnosis * Anti-HIV chemotherapy; subjects must be on a multi-drug regimen (excluding azidothymidine) and have an HIV viral load \< 50,000 copies/ml by reverse transcriptase-polymerase chain reaction (RT-PCR) at the time of study enrollment * Subjects must agree to have their anti-HIV regimen temporarily stopped, and then all subjects will stop antiretroviral therapy (ART) for approximately 7 days at the time they start filgrastim (G-CSF) post-chemotherapy for peripheral blood progenitor cell (PBPC) mobilization and until the mobilization is complete; in addition, if/when the CD4 counts return to a level of 450/mm\^3 with undetectable HIV levels in blood, the subjects will undergo an analytic treatment interruption for an indefinite period not to exceed 6 months * Karnofsky performance status \>= 70% * Biopsy proven intermediate grade or high-grade non-Hodgkin's lymphoma, including plasmablastic lymphoma, primary effusion lymphoma, or biopsy-proven Hodgkin's lymphoma (entities as defined in the World Health Organization \[WHO\] classification); tissue histology will be reviewed at the City of Hope; patients with prior marrow involvement must demonstrate =\< 10% involvement pre-stem cell collection * No psychosocial conditions that would hinder study compliance and follow-up * Pretreatment serum glutamic oxaloacetic transaminase (SGOT) and serum glutamic pyruvic transaminase (SGPT) =\< 2.5 x institutional upper limit of normal (ULN) * Serum bilirubin =\< 2.5 x institutional ULN * Patients who are hepatitis C virus (HCV) antibody positive or hepatitis B virus (HBV) surface antigen positive must be free of clinical evidence of cirrhosis that would otherwise make them ineligible for HCT, as determined by the Principal Investigator (PI) in consultation with the Gastrointestinal Service at City of Hope; patients with HBV and ongoing evidence of viral replication may require therapy prior to receiving high-dose chemotherapy * Serum creatinine =\< 2 x institutional ULN and a 24 hour urine creatinine clearance \>= 60 cc/min * Prothrombin time (PT)/partial thromboplastin time (PTT) =\< 2 x normal * Forced expiratory volume in 1 second (FEV1) or diffusion capacity of the lung for carbon monoxide (DLCO) \>= 50% predicted * Left ventricular ejection fraction (LVEF) \>= 50% (by 2-dimensional \[2-D\] echocardiogram or multigated acquisition scan \[MUGA\]); absence of cardiomyopathy, congestive heart failure or dysrhythmia * If the subject is female and of child-bearing potential, subject must have negative serum or urine pregnancy test within 7 days of treatment with research agent; men with partners of child-bearing potential and women of child-bearing potential, must be willing to use medically effective birth control methods, e.g. contraceptive pill, condom, or diaphragm and continue this for one year post HCT * Subjects must be on a prophylactic regimen for Pneumocystis carinii pneumonia, or agree to begin such treatment, if the CD4 counts are =\< 200 ELIGIBILITY CRITERIA (HODGKIN LYMPHOMA) - First or greater relapse after initial complete remission; or partial remission; or induction failure that responds to salvage therapy with stable disease, partial remission, or complete remission (i.e. chemosensitive disease) ELIGIBILITY CRITERIA (NON-HODGKIN LYMPHOMA): \- First complete remission with high risk features as specified by the International Prognostic Index, or Relapse after prior complete remission; partial remission; or induction failure that responds to salvage therapy with stable disease, partial remission, or complete remission (i.e. chemosensitive disease) SECONDARY ELIGIBILITY CRITERIA: * Subjects must complete both the therapeutic and research phases of the G-CSF mobilization of peripheral blood progenitor cells and * Subjects must have collected at least 5 x 10\^6 CD34+ cells/kg for the research phase of the collections Exclusion Criteria: * Presence of detectible HIV-1 that has C-X-C chemokine receptor type 4 (CXCR4)-tropism * Any symptomatic bacteria or fungal infection * AIDS related opportunistic infections within the past year for which treatment has been unsuccessful would be considered exclusionary but on a case-by-case basis as determined by the PI * Active cytomegalovirus (CMV) retinitis or other active CMV-related organ dysfunction; patients with a history of treated CMV infection are not excluded * Relapse of Pneumocystis carinii pneumonia within the past year * Intractable and severe diarrhea, defined as \> 1500 cc diarrheal fluid per day, or diarrhea causing persistent severe electrolyte abnormalities or hypoalbuminemia * Other AIDS-related syndromes, infectious or otherwise, if perceived to cause excessive risk for morbidity post-HCT, as determined by the PI * History of grade III hemorrhagic cystitis due to prior cyclophosphamide chemotherapy * Pregnant or nursing women * Any prior malignancy, except those treated with curative intent that are five years from treatment or cervical and anal squamous cell cancers or superficial basal cell and squamous cell cancers of skin * Active central nervous system (CNS) lymphoma; patients with a history of positive cerebrospinal fluid cytology that has become negative with intrathecal chemotherapy are eligible * Abnormal cytogenetics not related to the lymphoma * History of myocardial infarction or congestive heart failure * Any history of HIV-associated encephalopathy; dementia of any kind; seizures in the past 12 months; any perceived inability to directly provide informed consent (note: consent may not be obtained by means of a legal guardian) * Any medical or physical contraindication or other inability to undergo HPC-apheresis (HPC-A) collection * Elevated amylase or lipase SGOT, SGPT \> 2.5 x the institutional ULN * Serum bilirubin \> 2.5 x ULN * Any other laboratory value for complete blood count (CBC) and chemistry panel \> 2 x ULN