HIV-Resistant Gene Modified Stem Cells and Chemotherapy in Treating Patients With Lymphoma With HIV Infection

Inclusion Criteria:

* HIV-1 seropositive
* Stable, continuous antiretroviral treatment, defined as a multi-drug regimen (excluding zidovudine, also known as azidothymidine \[AZT\], Retrovir) prior to enrollment, as demonstrated by HIV plasma viral load \< 50 copies/mL
* Previously untreated non-Hodgkin lymphoma or Hodgkin lymphoma; all stages of disease are allowed; also eligible are patients who have started or completed one or more cycles of treatment as part of a planned first line regimen, or those who have received local radiation or surgery or corticosteroids for disease control
* Planned treatment with standard first line therapy for non-Hodgkin lymphoma (NHL) or Hodgkin lymphoma (HL)
* Karnofsky performance score \>= 70%
* Subjects must agree to use effective means to prevent conception 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 enrollment
* Subjects must be on a prophylactic regimen for Pneumocystis jiroveci pneumonia, or agree to begin such treatment, if CD4+ cell counts are observed to be =\< 200/ul in peripheral blood
* Able to understand, and the willingness to give, informed consent for the study

Exclusion Criteria:

* Central nervous system (CNS) lymphoma: CNS involvement by lymphoma, including parenchymal brain or spinal cord lymphoma or known presence of leptomeningeal disease prior to registration
* Patients with renal, hepatic, pulmonary, or cardiac disease that exclude delivery of standard chemotherapy
* Active (uncontrolled) infection requiring systemic antibiotic therapy with antibacterial, antifungal, or antiviral agents (excluding HIV)
* Hepatitis B surface antigen positive
* Hepatitis C virus (HCV) antibody positive and detectable HCV quantitative ribonucleic acid (RNA), with clinical evidence of cirrhosis as determined by the principal investigator
* Requiring active treatment for Toxoplasma gondii infection
* Malignancy other than lymphoma, unless (1) in complete remission and more than 5 years from last treatment, or (2) cervical/anal squamous cell carcinoma in situ or (3) superficial basal cell and squamous cell cancers of the skin
* 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 concurrent or past medical condition that, in the opinion of the investigator, would exclude the subject from participation
* Patients who have received a vaccine for HIV-1 or any prior gene modified cell product, at any time
* A medical history of noncompliance with HAART or medical therapy
* Pregnant women or nursing mothers
* Use of zidovudine as part of the HAART regimen (a drug substitution for zidovudine at the time of study entry is allowed)
* Known hypersensitivity to any of the products used in the trial - G-CSF (Neupogen, filgrastim), plerixafor (Mozobil), or any components of the chemotherapeutic agents or O6BG/BCNU in vivo selection regimens