Gene Therapy After Frontline Chemotherapy in Treating Patients With AIDS-Related Non-Hodgkin Lymphoma

Inclusion Criteria: * HIV-1 seropositive at or before the time of lymphoma diagnosis * Karnofsky performance status \>= 70% * Biopsy proven NHL, including plasmablastic lymphoma and primary effusion lymphoma but not T-cell lymphoma; tissue histology will be reviewed at City of Hope (COH); patients who have been in remission for \> 1 year post Hodgkin's lymphoma chemotherapy are also considered eligible * \>= 28 days from completion of frontline chemotherapy for NHL * If remission status \< 1 year for NHL, complete remission documented by computed tomography (CT) or positron emission tomography (PET)-CT scan within 3 months of study entry * No diagnosed psychosocial conditions that would hinder study compliance and follow-up * Pretreatment serum glutamic oxaloacetic transaminase (SGOT), serum glutamate pyruvate transaminase (SGPT) =\< 2.5 x institutional upper limit of normal (ULN) * Pretreatment serum bilirubin =\< 2.5 x institutional ULN or - Total bilirubin \< 4.5 mg/dl with direct fraction =\< 0.3 mg/dl in patients for whom these abnormalities are felt to be due to protease inhibitor therapy * Serum creatinine \< 2 x the institutional ULN * Absence of clinically significant cardiomyopathy, congestive heart failure * Cardiac ejection fraction has to be \>= 50% * Spirometry diffusion capacity (diffusion capacity of the lung for carbon monoxide \[DLCO\]) \>= 50% * 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 HSPC infusion * 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 cells/uL SECONDARY ELIGIBILITY CRITERIA FOR GENE-MODIFIED HSPC INFUSION: * Subjects must complete the filgrastim (G-CSF)/plerixafor mobilization of peripheral blood progenitor cells and must have collected at least 7.5 x 10\^6 CD34+ cells/kg, sufficient for preparation of both, a back-up of 2.5 x 10\^6 CD34+ cells and the research product * Research product must pass all release tests * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for six months following duration of study participation; should a woman become pregnant or suspect that she is pregnant while participating on the trial, she should inform her treating physician immediately * All subjects must have the ability to understand and the willingness to sign a written informed consent Exclusion Criteria: * Any AIDS-related opportunistic infection occurring within the past year and for which treatment has been unsuccessful would be considered exclusionary, but this is done on a case-by-case basis as determined by the principal investigator * Active cytomegalovirus (CMV) retinitis or other active CMV-related organ dysfunction; patients with a history of treated CMV infection are not excluded * Patients who are hepatitis C virus (HCV) antibody positive and HCV ribonucleic acid (RNA) or hepatitis B virus (HBV) surface antigen positive and HBV DNA positive * Pregnant or nursing women * Active central nervous system (CNS) lymphoma, history of HIV-associated encephalopathy; dementia of any kind; seizures in the past 12 months; patients with a history of positive cerebrospinal fluid cytology that has become negative with intrathecal chemotherapy and the patient has been in remission for at least 12 months are eligible * Any history of HIV-1 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 any other inability to undergo HSPC collection * Patients should not have any uncontrolled illness including ongoing or active infection * Patients may not be receiving any other investigational agents, or concurrent biological, chemotherapy, or radiation therapy * History of allergic reactions attributed to compounds of similar chemical or biologic composition to G-CSF/filgrastim (Escherichia \[E\] coli producing cell line), plerixafor or busulfan * Patients with other active malignancies other than skin cancers are ineligible for this study * Subjects, who in the opinion of the investigator, may not be able to comply with the safety monitoring requirements of the study will be considered non-compliant