Iodine I 131 Monoclonal Antibody BC8 Before Autologous Stem Cell Transplant in Treating Patients With Relapsed or Refractory Hodgkin Lymphoma or Non-Hodgkin Lymphoma

Inclusion Criteria:

* Patients must have a histologically confirmed diagnosis of B-NHL, T-NHL, or HL; CD45 antigen expression must be documented on tumor specimens in all cases except HL, in whom histologic demonstration of CD45+ cells adjacent to the Reed Sternberg cells is required
* Patients must have received at least one prior standard systemic therapy with documented recurrent or refractory disease
* Mantle cell lymphoma (MCL), T-NHL, or other high-risk malignancies may be enrolled/transplanted in complete remission (CR)/first partial remission (PR1)
* Patients are preferred to have either a tumor mass amenable to core needle biopsy during the dosimetry phase, or a measurable tumor mass with at least one site of involvement measuring 2.0 cm in largest dimension on computed tomography (CT) imaging for purposes of planar and/or single-photon emission CT (SPECT)/CT tumor dosimetry (patients with disease that does not allow tumor dosimetry will be allowed on study since they still can contribute toward achieving the primary endpoint, but these patients will be given a lower priority over those with evaluable disease)
* Creatinine \[Cr\] \< 2.0
* Bilirubin \< 1.5 mg/dL, with the exception of patients thought to have Gilbert's syndrome, who may have a total bilirubin above 1.5 mg/dL
* All patients eligible for therapeutic study must have a minimum of \>= 4 x10\^6 CD34/kg autologous hematopoietic stem cells harvested and cryopreserved and divided into 2 aliquots of at least \>= 2 x10\^6 CD34/kg each; patients with a history of prior autologous hematopoietic cell transplant (HCT) are only required to have \>= 2x10\^6 CD34/kg stored
* Patients must have an expected survival of \> 60 days and must be free of major infection

Exclusion Criteria:

* Circulating human anti-mouse antibody (HAMA), to be determined before each infusion
* Systemic anti-lymphoma therapy given in the previous 30 days before the scheduled therapy dose with the exception of rituximab
* Inability to understand or give an informed consent
* Lymphoma involving the central nervous system
* Other serious medical conditions considered to represent contraindications to bone marrow transplant (BMT) (e.g. abnormally decreased cardiac ejection fraction, diffusion capacity of the lung for carbon monoxide (DLCO) \< 50% predicted, forced expiratory volume in one second (FEV1) \< 70% predicted, acquired immune deficiency syndrome \[AIDS\], etc.)
* Known human immunodeficiency virus (HIV) seropositivity
* Pregnancy or breast feeding
* Prior allogeneic bone marrow or stem cell transplant
* Prior autologous bone marrow or stem cell transplant or prior radiation therapy (RT) \> 20 Gy to a critical organ within 1 year of enrollment
* 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/unselected PBSC are to be used (patients with cryopreserved stem cells which are negative \[=\< 0.1% involved\] by flow cytometry will also be considered eligible)
* Southwest Oncology Group (SWOG) performance status \>= 2.0
* Unable to perform self-care during radiation isolation
* Expected survival if untreated less than 60 days