Inclusion Criteria:
* HIV seropositive at or before the time of lymphoma diagnosis
* Subjects must be on a multi-drug regimen (excluding azidothymidine) to maintain HIV viral load less than 50,000 Gc/mL; if the CD4 count at enrollment is less than 100 then the viral load should be less than 10,000 by reverse transcriptase polymerase chain reaction (Rt-PCR); if the CD4 count is greater than 100/mm\^3 prior to the start of any lymphoma chemotherapy and is greater than 100/mm\^3 for at least 3 months then the viral load must be less than 150,000 gc/ml and clinically stable; if no pre-chemotherapy CD4 counts are available, then viral load alone will be used from enrollment
* The known hematopoietic toxicity of AZT (zidovudine) prohibits its use pre-transplant during stem cell collection and during the immediate period of engraftment post-transplant; resumptions of AZT should not begin until there is evidence of stable engraftment; therefore, AZT should not be resumed until at least 2 months after last blood product support is used; since platelet support continues until approximately day +14 days in our experience with acquired immune deficiency syndrome (AIDS) patients transplanted date, AZT will be prohibited until at least 2 months after transplant; therefore, if the anti-HIV drug combination needs to be modified then AZT can be part of the new regimen
* Karnofsky performance status \>= 70%
* Biopsy proven intermediate grade or high-grade Non-Hodgkin's lymphoma, (working formulation groups D-H and J, and Plasmablastic lymphoma of any disease state, including first remission given the poor risk nature of this histology) or Hodgkin's lymphoma of any subtype except nodular lymphocytic and histiocytic (L\&H) lymphocyte predominant; tissue histology will be reviewed at the City of Hope
* Patients with prior marrow involvement must demonstrate \< 10% involvement (by morphology) pre stem cell collection
* Pretreatment serum glutamic oxaloacetic transaminase (SGOT) and serum glutamic pyruvate transaminase (SGPT) \< 1.5 x institutional upper limit of normal
* Serum bilirubin \< 1.5 x institutional upper limit of normal
* Patients who are Hepatitis C antibody positive or Hepatitis B surface antigen positive without clinical evidence of cirrhosis will be eligible after further evaluation; specifically, if patient hepatitis C or B positive viral loads will be measured; patients with hepatitis B and ongoing evidence of viral replication may require therapy prior to receiving high dose chemotherapy; this decision will be at the discretion of the treating physician
* Serum creatinine \< 2 x institutional upper limit of normal and a 24 hour urine creatinine clearance \> 60 cc/min
* Prothrombin time (PT)/partial thromboplastin time (PTT) \< 2 x normal
* Forced expiratory volume in one second (FEV1) or diffusing capacity of the lung for carbon monoxide (DLCO) \>= 50% predicted
* Left ventricular ejection fraction (LVEF) \>= 50% (by 2 dimensional \[2 D\] echocardiogram or multi gated acquisition scan \[MUGA\] scan); absence of cardiomyopathy, congestive heart failure or dysrhythmia
* If female of child bearing potential, must have negative serum pregnancy test
* Subjects must be on a prophylactic regimen for pneumocystis pneumonia if the CD4 counts are \< 200
* Subjects who are not in complete remission must have measurable disease; measurable disease means that there are bidimensionally measurable lesions with clearly defined margins using either a medical photograph, computerized axial tomography (CAT) scan or magnetic resonance imaging (MRI) scan, or palpation of lesions with both diameters \>= 2 cm; evaluable disease means that the lesions are only unidimensionally measurable, or have indistinct margins or have both diameters \< 0.5 cm, or that the palpable lesions have a diameter \< 2.0 cm, or are lesions in bone; pleural effusions and ascites are considered nonevaluable disease; scans must be within 28 days from enrollment
* A minimum of 2.5 x 10\^6 CD34 cells/kg must have been collected
* Hodgkin's Lymphoma:
* Partial response after standard chemotherapy OR
* First relapse after initial complete remission with standard chemotherapy
* Non-Hodgkin's Lymphoma:
* First complete remission after standard chemotherapy with high risk features as specified by the International Prognostic Index;
* Partial response after standard chemotherapy; OR
* Relapse after initial complete remission with standard chemotherapy
Exclusion Criteria:
* Active bacterial or fungal infection
* AIDS related opportunistic infection within past year, excluding treatment-responsive Mycobacterium Avium Intracellular infection, and treatment-responsive oral thrush, herpes simplex or herpes zoster
* Active cytomegalovirus (CMV) retinitis or other CMV-related organ dysfunction; patients with a history of treated CMV infection are not excluded
* Relapse of pneumocystis carinii pneumonia within the past year
* AIDS related syndromes or symptoms that pose a perceived excessive risk for transplantation-related morbidity as determined by the principle investigator
* Intractable and severe diarrhea as defined as \> 1500 cc diarrheal fluid per day of diarrhea causing persistent severed electrolyte abnormalities or hypoalbuminemia
* History of grade III hemorrhagic cystitis due to prior chemotherapy
* Pregnant or nursing women
* Any prior malignancy except treated basal cell carcinoma of the skin; females with cervical dysplasia may be included at the discretion of the treating physician and the principle investigator
* Patients with a history of positive cerebrospinal fluid (CSF) cytology that has become negative with intrathecal chemotherapy are eligible; patients should have a negative spinal fluid cytology within thirty days prior to enrollment
* Abnormal cytogenetics on screening bone marrow biopsy
* Psychosocial conditions that hinder compliance
