Iodine I 131 Tositumomab, Etoposide and Cyclophosphamide Followed by Autologous Stem Cell Transplant in Treating Patients With Relapsed or Refractory Non-Hodgkin's Lymphoma

Inclusion Criteria: * Patients must have a histologically confirmed diagnosis of lymphoma expressing the cluster of differentiation (CD)20 antigen and generally must have failed at least one prior standard systemic therapy; the exception will be mantle cell lymphoma (MCL) patients, who may be enrolled while in first complete remission (CR) in accordance with current transplant standard of care for these patients * Note: Patients with clinically non-transformed follicular lymphomas do not require repeat biopsies for immunophenotyping since these tumors are uniformly reactive with the tositumomab antibody * Patients must have tumor burdens \< 500cc by computed tomography (CT) or magnetic resonance (MRI) volumetric measurements and must not have splenomegaly at the time of enrollment; splenomegaly will be defined as a spleen volume \> 2 standard deviations of the mean spleen volume to body weight ratio (mean = 3.84 cc/kg, SD = 1.53 cc/kg); thus, patients with \> 6.9cc/kg will be defined as having splenomegaly; patients with splenomegaly that is thought to be due to G CSF/GM-CSF effect and not due to lymphomatous involvement of the spleen can been deemed eligible with the approval of an investigator * Patients must have normal renal function (creatinine \[Cr\] \< 2.0) * Patients must have normal hepatic function (bilirubin \< 1.5mg/dL), with the exception of patients thought to have Gilbert's syndrome, who may have a total bilirubin above 1.5mg/dL * All patients eligible for therapeutic study must have autologous hematopoietic stem cells (2 x 10\^6 CD34+ cells/kg) harvested and cryopreserved * Patients must have an expected survival of \> 60 days and must be free of major infection Exclusion Criteria: * Circulating anti-mouse antibody (HAMA) * Systemic anti-lymphoma therapy given within 30 days prior to anticipated treatment date * Inability to understand or give an informed consent * Prior radiation \> 20 Gy to any critical normal organ (e.g., lung, liver, spinal cord, or over 25% of red marrow) * Central nervous system lymphoma * Other serious medical conditions considered to represent contraindications to autologous stem cell transplant (ASCT) (e.g., active coronary artery disease, pulmonary dysfunction \[forced expiratory volume in 1 second (FEV1) \< 70% expected, Vital Capacity \< 70% expected, diffusing capacity of the lung for carbon monoxide (DLCO) \< 50%, patient on supplemental oxygen\], AIDS, etc.) * Pregnancy * Prior bone marrow or stem cell transplant * Presence of circulating lymphoma cells by morphology or flow cytometry (\>= 0.1%) at or near the time of peripheral blood stem cell (PBSC) collection if unpurged PBSC are to be used * Southwest Oncology Group (SWOG) performance status \>= 2.0 * Unable to perform self-care during radiation isolation * Patients with chronic lymphocytic leukemia (CLL) or small lymphocytic lymphoma/well differentiated lymphocytic lymphoma (ineligible because these tumors express very low surface densities of CD20)