Re-Induction Therapy for Relapsed Pediatric T-Cell Acute Lymphoblastic Leukemia or Lymphoma

This is a study of re-induction therapy that will comprise of three blocks of multi-agent chemotherapy. CR will be evaluated following each block of therapy. All patients will be candidates for hematopoietic stem cell transplant (HSCT) once they achieve negative minimal residual disease (MRD). If patients cannot proceed to HSCT following Block A, they will continue therapy on Block B and Block C until ready for HSCT. Three Block Induction: Block A: approximately 5 weeks * Dexamethasone 10 mg/m\^2/day orally (PO) Days 1-8, 15-22 (Total 16 days) * Panobinostat 24 mg/m\^2/dose PO Day 2,4,6 * Liposomal vincristine (VSLI) 2.25 mg/m\^2 no cap intravenously (IV) on Days 7, 14, 21, 28 * Mitoxantrone 10 mg/m\^2 IV Day 7,14 (In the absence of peripheral blasts, Day 14 Mitoxantrone will be given if WBC ≥1000 and ANC ≥300) * Peg-asparaginase 2500 units/m\^2 on Days 9,23 * Bortezomib 1.3 mg/m\^2 IV Days 16, 19, 23, 26 * Intrathecal Triples (IT) (intrathecal methotrexate/hydrocortisone/cytarabine) (ITMHA) Days 1, 7, 14, 21, 28. Additional ITs on Days 10 and 17 for patients with central nervous system (CNS) 2, 3 or traumatic tap with blasts Block B: approximately 5 weeks * High-dose methotrexate 8 g/m\^2 IV over 24 hours (will not be given to patients with prior cranial irradiation) Day 1 * 6-mercaptopurine 50 mg/m\^2 PO days 1-14 * ITMHA Day 1 * High-dose cytarabine 3 g/m\^2 IV every 12 hours (Q12H) Days 15 and 16 Block C: approximately 3 weeks * Nelarabine 650 mg/m\^2/day IV Days 1-5 (Clofarabine 40 mg/m\^2/day IV Days 1-5 will be given instead of nelarabine for patients with B-lymphoblastic leukemia and lymphoma in stratum II) * Cyclophosphamide 300 mg/m\^2 IV Days 1-5 * Etoposide 100 mg/m\^2/day IV Days 1-5 Response evaluation is performed after the end of each treatment block. All patients should proceed to hematopoietic stem cell transplantation (HSCT) after achieving negative minimal residual disease (MRD) when a suitable donor is identified. Patients could continue on Block B and Block C if not ready for HSCT. If after completion of Block C, MRD is persistently positive, the plan will be discussed with the principal investigator and co-principal investigator and the transplant team. Enrollment on ongoing natural killer (NK) cell studies will be considered. For patients who require a second transplant, HAP3R (another clinical trial at St. Jude Children's Research Hospital) may be an option. Donor will be selected according to institutional practices and transplant regimens will be used according to institutional HSCT protocols and guidelines.