Yttrium Y 90 Basiliximab and Combination Chemotherapy Before Stem Cell Transplant in Treating Patients With Mature T-cell Non-Hodgkin Lymphoma

Inclusion Criteria: * Patients with a pathologically confirmed diagnosis of systemic mature T-cell non-Hodgkin lymphoma (NHL) with City of Hope pathology review as per World Health Organization (WHO) classification of lymphomas 2008, who are deemed eligible for high dose therapy and AHCT including patients in: \* T-NHL histologies including peripheral T-cell lymphomas (PTCLs), cutaneous T-cell lymphomas (CTCLs) and natural killer (NK)/T cell lymphomas * First remission after initial first-line therapy (CR1) in PTCL patients, except for anaplastic lymphoma receptor tyrosine kinase (ALK)+ anaplastic large cell lymphoma (ALCL) and CTCL; patients with minimal residual disease after induction therapy may also be eligible at the discretion of the principal investigator (PI) * Relapsed/refractory disease, stable disease, partial remission (PR) or complete remission (CR), who have received at least 2 lines of therapy, and do not have an adequate allogenetic stem cell transplant option * Life expectancy \>= 6 months * Karnofsky status \>= 70% * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for six months following duration of study participation; should a woman become pregnant or suspect that she is pregnant while participating on the trial, she should inform her treating physician immediately * 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 diffusing capacity of the lung for carbon monoxide (DLCO) \> 50% of predicted measured * Bilirubin \< 1.5 x normal except in cases where abnormal liver function tests (LFTS) are due to involvement with T-NHL * Serum glutamic oxaloacetic transaminase (SGOT) AND serum glutamate pyruvate transaminase (SGPT) \< 2 x normal except in cases where abnormal LFTS are due to involvement with T-NHL * Serum creatinine of \< 1.5 mg/dL, and a measured creatinine clearance of \> 60 mL/min * Patients will be enrolled at 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 * Recovery from non-hematologic toxicities of salvage cytoreductive chemotherapy to =\< grade 2 (Common Terminology Criteria for Adverse Events \[CTCAE\] version 4 \[v4\]) * Body mass index (BMI) \> 35% will be considered on a case-by-case basis by the Radiation Oncology principal investigator (P.I.) * All subjects must have the ability to understand and the willingness to sign a written informed consent * Systemic chemotherapy or radiation cannot have been given within 4 weeks prior to the Y-90 dose of radioimmunotherapy (RIT), with the exception of single agent cyclophosphamide priming chemotherapy administered for mobilization Exclusion Criteria: * Progressive disease * Patients should not have any uncontrolled illness including ongoing or active infection requiring therapy * Patients may not be receiving any other investigational agents, or concurrent biological, chemotherapy, or radiation therapy; may have received an experimental agent prior to enrolling in the trial * History of allergic reactions attributed to compounds of similar chemical or biologic composition to basiliximab * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with indium In 111 (111In-) and 90Y-basiliximab-DOTA * Prior high dose chemotherapy for autologous hematopoietic cell transplantation 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 the lung will be ineligible; patients with ANY prior radiation to the heart are ineligible; patients with \> 500 cGy to the kidney will be excluded from the study; Note: patients who have had electron beam therapy are still eligible and will be evaluated on a case by case basis by the Radiation Oncology PI * Presence of antibody against basiliximab in serum (only required for patients who have received prior antibody) * Research participants with presence of other active malignancy; however, research participants with history of prior malignancy treated with curative intent and in complete remission are eligible; any history of myelodysplasia is excluded * Active hepatitis B or C viral infection or hepatitis B surface antigen positive * Patients with a detectable human immunodeficiency virus (HIV) viral load or who are HIV-positive AND have a resistant genotype * Patients with psychosocial circumstances or illnesses that preclude protocol participation (to be determined by P.I.) * 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) * Evidence of marrow disease by flow and morphology after upfront or salvage cytoreductive therapy and before stem cell mobilization * Bone marrow (BM) harvest required to reach adequate cell dose for transplant * Subjects, who in the opinion of the investigator, may not be able to comply with the safety monitoring requirements of the study