Inclusion Criteria:  Documented informed consent of the participant and/or legally authorized representative  Assent, when appropriate, will be obtained per institutional guidelines Age: >= 18 years Karnofsky performance status >= 70% Life expectancy >= 6 months Histologically confirmed Hodgkin lymphoma (HL)  Relapsed/refractory disease  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 partial response (PR) or complete response (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 different salvage therapy regimens to attain CR In 2nd or subsequent RL whether in CR or not after salvage therapy  High risk relapsed or refractory HL disease defined as having any one of the following:  B symptoms at relapse Extranodal disease at relapse Primary refractory disease Relapse < 1 year after completion of frontline therapy Not in CR at the time of transplant Relapse after receiving PD1 blockade or brentuximab vedotin as initial therapy Patients will be enrolled after collection of at least 2.0 x 10^6 CD34 cells/kg of autologous hematopoietic progenitor cells (HPC-A) by apheresis Recovery from non-hematologic toxicities of salvage cytoreductive chemotherapy to =< grade 2 (Common Terminology Criteria for Adverse Events [CTCAE] version [v]5) Serum creatinine =< 1.5 mg/dL (performed prior to day 1 of protocol therapy) Creatinine clearance of >= 60 mL/min per 24 hour urine test =< 1.5 mg/dL (performed prior to day 1 of protocol therapy) Total bilirubin =< 1.5 X upper limit of normal (ULN) (unless has Gilbert's disease) (performed prior to day 1 of protocol therapy) Aspartate aminotransferase (AST)/serum glutamic-oxaloacetic transaminase (SGOT) =< 1.5 x ULN (except in cases where abnormal liver function tests (LFTs) are due to involvement with HL) (performed prior to day 1 of protocol therapy) Alanine aminotransferase (ALT)/serum glutamate pyruvate transaminase (SGPT) =< 1.5 x ULN (except in cases where abnormal LFTs are due to involvement with HL) (performed prior to day 1 of protocol therapy) Left ventricular ejection fraction (LVEF) >= 50% (performed prior to day 1 of protocol therapy) Forced expiratory volume in 1 second (FEV1) > 65% of predicted measured, or DLCO (diffusion capacity) >= 50% of predicted measured (corrected for hemoglobin) (performed prior to day 1 of protocol therapy)  Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least six months after the last dose of protocol therapy  Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for > 1 year (women only)  Exclusion Criteria:  Planned BV consolidation after AHCT 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 principal investigator (PI) Patients may not be receiving any other investigational agents, or concurrent biological, chemotherapy, or radiation therapy Myelodysplasia or any active malignancy other than HL, or < 5 years remission from any other prior malignancy, except non-melanoma skin cancer, localized prostate cancer or localized cervical cancer 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) Lymphocyte-predominant Hodgkin lymphoma History of allergic reactions attributed to compounds of similar chemical or biologic composition to 90Y-basiliximab-DOTA Presence of antibodies against basiliximab (only required for patients who have received prior antibody therapy) Persistent marrow involvement (> 10%) with HL after salvage cytoreductive therapy and before stem cell mobilization Bone marrow (BM) harvest required to reach adequate cell dose for transplant Active hepatitis B or C viral infection or hepatitis B surface antigen positive Positive human immunodeficiency virus antibody, patients with undetectable human immunodeficiency virus (HIV) viral load with CD4 >= 300 and are on highly active antiretroviral therapy (HAART) medication are allowed Patients should not have any uncontrolled illness including ongoing or active infection Patients with psychosocial circumstances or illnesses that preclude protocol participation (to be determined by P.I.) Pregnant women are excluded from this study because 90Y-basiliximab/DOTA is an agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother 90Y-basiliximab/DOTA, breastfeeding should be discontinued if the mother is treated with 90Y-basiliximab/DOTA Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)