Chemoimmunotherapy and Allogeneic Stem Cell Transplant for NK T-cell Leukemia/Lymphoma

Inclusion Criteria: * Patients must weigh at least 10 kilograms at the time of the study enrollment. * Diagnosis Newly diagnosed patients with histologically proven mature T- and NK- cell neoplasms: COHORT 1 * Aggressive NK cell leukemia (ICD-O code 9948/3) * Extranodal NK/T-cell lymphoma, nasal type (ICD-O code 9719/3) COHORT 2 * Enteropathy-associated T-cell lymphoma (ICD-O code 9717/3) * Hepatosplenic T-cell lymphoma (ICD-O code 9716/3) * Peripheral T-cell lymphoma, non-otherwise specified (ICD-O code 9702/3) * Angioimmunoblastic T-cell lymphoma (ICD-O code 9705/3) * Other mature T- and NK-cell neoplasm histologies will considered after case-by-case discussion with Study Chairs and executive Vice-Chair Patients with lymphoma must have stage III or IV disease (See Appendix III for Staging). * Organ Function Requirements Adequate liver function defined as: * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) for age. * ALT (SGPT) \< 3 x ULN for age. Adequate cardiac function defined as: * Shortening fraction of ≥ 27% by echocardiogram, or * Ejection fraction of ≥ 50% by radionuclide angiogram. Adequate pulmonary function defined as: • Patients with a history of pulmonary dysfunction must have no evidence of dyspnea at rest, no exercise intolerance due to pulmonary insufficiency, and a pulse oximetry \> 92% while breathing room air unless current dysfunction is due to the lymphoma, in which case the patient is eligible. Exclusion Criteria: * Alk+ or Alk- Anaplastic Large Cell Lymphoma (ALCL) * Patients with active CNS disease. * Patients with stage I or stage II disease (See Appendix III for Staging). * Patients who have received any prior cytotoxic chemotherapy for the current diagnosis of NHL. * Previous steroid treatment and/or radiation treatment are not allowed unless they are used for emergency management. Patients who have received emergency irradiation and/or steroid therapy will be eligible only if started on protocol therapy not more than one week from the start of radiotherapy or steroids. * Female patients who are pregnant. Pregnancy tests must be obtained in girls who are post menarchal. * Lactating females, unless they have agreed not to breastfeed their infants. * Patients with Down syndrome. * Patients taking CYP3A4 substrates with narrow therapeutic indices. Patients (COHORT 2 ONLY) chronically receiving medications known to be metabolized by CYP3A4 and with narrow therapeutic indices (See Appendix V). The topical use of these medications (if applicable) is allowed. * Patients taking CYP3A4 inhibitors. Patients (COHORT 2 ONLY) chronically receiving drugs that are known potent CYP3A4 inhibitors within 7 days prior to study enrollment (See Appendix V). The topical use of these medications (if applicable) is allowed. * Patients taking CYP3A4 inducers. Patients (COHORT 2 ONLY) chronically receiving drugs that are known potent CYP3A4 inducers within 12 days prior to study enrollment (See Appendix V).