Iodine I 131 Tositumomab and Fludarabine Phosphate in Treating Older Patients Who Are Undergoing an Autologous or Syngeneic Stem Cell Transplant for Relapsed or Refractory Non-Hodgkin's Lymphoma

Inclusion Criteria:

* Patients must have a histologically confirmed diagnosis of lymphoma expressing the CD20 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
* Creatinine (Cr) \< 2.0
* Bilirubin \< 1.5 mg/dL, with the exception of patients thought to have Gilbert's syndrome, whom may have a total bilirubin above 1.5 mg/dL
* All patients eligible for therapeutic study must have (\>= 2x10\^6 CD34/kg) autologous hematopoietic stem cells harvested and cryopreserved, or this number of cells harvested from a syngeneic donor
* Patients must have an expected survival of \> 60 days and must be free of major infection
* DONOR: Syngeneic donors must be confirmed syngeneic by ABO typing, human leukocyte antigen (HLA) typing, and variable number tandem repeat (VNTR) analysis
* DONOR: Syngeneic donors must meet eligibility under Standard Practice Guidelines/Standard Treatment

Exclusion Criteria:

* Circulating anti-mouse antibody (HAMA) (to be determined before both dosimetry and therapy)
* Systemic anti-lymphoma therapy given in the previous 30 days before the scheduled therapy dose
* Inability to understand or give an informed consent
* Prior radiation \> 20 Gy to any critical normal organ (e.g., lung, liver, spinal cord, \> 25% of red marrow)
* Central nervous system lymphoma
* Other serious medical conditions considered to represent contraindications to bone marrow transplant (BMT) (e.g., abnormally decreased cardiac ejection fraction, diffusing capacity (DLCO) \< 50% predicted, patient on supplemental oxygen, acquired Immunodeficiency syndrome \[AIDS\], etc.)
* Pregnancy
* Prior bone marrow or stem cell transplant
* South West Oncology Group (SWOG) performance status \>= 2
* Unable to perform self-care during radiation isolation
* Patients with chronic lymphocytic leukemia (CLL) or small lymphocytic lymphoma/well differentiated lymphocytic lymphoma