This phase I trial studies the side effects and best dose of yttrium Y 90 basiliximab when given together with standard combination chemotherapy before a stem cell transplant in treating patients with mature T-cell non-Hodgkin lymphoma. Radioactive substances linked to monoclonal antibodies, such as yttrium Y 90 basiliximab, can bind to cancer cells and give off radiation which may help kill cancer cells. Drugs used in chemotherapy, such as carmustine, cytarabine, etoposide, and melphalan (BEAM), work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving yttrium Y 90 basiliximab and chemotherapy before a stem cell transplant may help kill any cancer cells that are in the body and help make room in the patient's bone marrow for new blood-forming cells (stem cells) to grow. Stem cells that were collected from the patient's blood and stored before treatment are later returned to the patient to replace the blood-forming cells that were destroyed.