Autologous Peripheral Stem Cell Transplant in Treating Patients With Non-Hodgkin's Lymphoma or Hodgkin's Lymphoma

Inclusion Criteria: * Karnofsky performance status: \>80% (\>60% if poor performance status is related to lymphoma) * No evidence of serious organ dysfunction that is not attributable to tumor * Central nervous system: Patients with a history of CNS involvement by lymphoma or with relapsed primary lymphoma will be eligible. * Infection: Patients with serious uncontrolled infections at the time of transplant will be excluded. * Hepatitis B: Patients who are carriers of Hepatitis B will be included in this study. These patients are not eligible to receive rituximab as a component of their chemotherapy mobilization. * HIV disease. Patients with HIV disease are eligible for this study provided that: * Patients will be seen in the infectious disease (ID)/HIV clinic prior to enrollment on study for the purpose of determining eligibility and for local coordination of HIV care during the peri-transplant period. * Must be on a maximally active anti-HIV regimen * CD4+ ≥ 50/μL * HIV RNA viral load ≤ 100,000 copies per mL on each of samples 4 weeks apart. The most recent level must be within one month of enrollment. * Non-Hodgkin's lymphoma (NHL). Patients with chemo-sensitive histologically confirmed NHL. * Precursor B-cell or Precursor T-cell NHL * Lymphoblastic lymphoma * All patients will be eligible in second or greater complete remission (CR) or first or subsequent partial remission (PR) * Mature B-cell Lymphomas: * Small lymphocytic lymphoma (S…