Radiolabeled Monoclonal Antibody Therapy and Combination Chemotherapy Before Stem Cell Transplant in Treating Patients With Primary Refractory or Relapsed Hodgkin Lymphoma

Inclusion Criteria:

* Pathology confirmation of HL with City of Hope (COH) pathology review
* Hodgkin lymphoma that is:

  * PIF (primary induction failure): did not enter complete remission with first line of therapy; Note: a patient with PIF who responds to salvage therapy with a PR or CR is also eligible (and would be considered PIF-sensitive)
  * Early 1st relapse: initial CR of \> 3 months and \< 12 months after 1st line chemotherapy
  * 1st relapsed HL in a patient who is not in CR after 2 cycles of salvage therapy
  * In 2nd or subsequent relapse (RL) whether in CR or not after salvage therapy
* Relapse/persistent disease evidenced by a computed tomography and fluorodeoxyglucose (FDG)-positron emission tomography (PET), or bone marrow biopsy
* Cardiac ejection fraction of \>= 50% by echocardiogram or multi gated acquisition scan (MUGA)
* Forced expiratory volume in one second (FEV1) \> 65% of predicted measured, or diffusion capacity of the lung for carbon monoxide (DLCO) \>= 50% of predicted measured
* Bilirubin =\< 1.5 x normal
* Serum glutamic oxaloacetic transaminase (SGOT) or serum glutamate pyruvate transaminase (SGPT) =\< 2 x normal except in cases where abnormal liver function tests (LFTS) are due to involvement with HL
* Serum creatinine of =\< 1.5 mg/dL, and a measured creatinine clearance of \>= 60 mL/min
* Karnofsky status \>= 70%
* Life expectancy \>= 6 months
* Females must not be pregnant or breast feeding, and must use accepted birth control methods; males must use accepted birth control methods
* Capability of providing informed consent
* Patients will be enrolled after receiving at least two cycles of salvage cytoreductive chemotherapy and collection of at least 3.0 x 10\^6 CD34 cells/kg of autologous hematopoietic progenitor cells (HPC-A) by apheresis; a minimum of 2 collection procedures is required, unless collection on day #1 \> 5.0 x 10\^6 CD34 cells/kg; a maximum of 10 collections is allowed; bone marrow harvest to supplement apheresis is not allowed
* Co-enrollment on Institutional Review Board (IRB) #98117, entitled Molecular Pathogenesis of Therapy-Related Leukemia
* All pre-study and follow-up imaging studies preferably performed at City of Hope
* Recovery from non-hematologic toxicities of salvage cytoreductive chemotherapy to =\< grade 2 (Common Terminology Criteria for Adverse Events version 4 \[CTCAE v4\])
* Body mass index (BMI) \> 30% will be considered on a case-by-case basis by the radiation oncology principal investigator (PI)
* While on this study, patients may not be treated with any other investigational agent for any purpose until relapse or progression

Exclusion Criteria:

* Lymphocyte-predominant Hodgkin lymphoma
* Prior high dose chemotherapy with autologous stem cell transplant, or prior allogeneic transplantation
* Significant prior external beam dose-limiting radiation to a critical organ based on review of the prior radiation treatment records by the radiation oncology PI; patients who have had prior external beam radiation \> 2000 cGy (at 180 to 200 cGy per day) to any portion of the lung will be ineligible; patients with ANY prior radiation to the heart are ineligible; patients with \> 500 cGy to any portion of the kidney will be excluded from the study
* Presence of antibody against basiliximab (only required for patients who have received prior antibody)
* Myelodysplasia or any active malignancy other than HL, or \< 5 years remission from any other prior malignancy, except adequately treated basal cell or squamous cell carcinoma
* Active hepatitis B or C viral infection or hepatitis B surface antigen positive
* Positive human immunodeficiency virus antibody
* Patients with psychosocial circumstances or illnesses that preclude protocol participation (to be determined by PI)
* Co-morbid illnesses that preclude protocol participation (to be determined by PI)
* Any cytogenetic abnormality in the bone marrow that is known to be associated with or predictive of myelodysplasia is excluded. This includes, but is not limited to, del(5), del(7), del(11)
* Persistent marrow involvement (\> 10%) with HL after salvage cytoreductive therapy and before stem cell mobilization
* Systemic chemotherapy or radiation within 4 weeks prior to the Y-90 dose of radioimmunotherapy (RIT), with the exception of single agent Cytoxan priming chemotherapy administered for mobilization
* Bone marrow (BM) harvest required to reach adequate cell dose for transplant