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…