Pevonedistat With VXLD Chemotherapy for Adolescent/Young Adults With Relapsed/Refractory ALL or Lymphoblastic NHL

Inclusion Criteria: 1. Male or female patients 16-39 years of age (AYA). 2. Patients must have a diagnosis of a relapsed / refractory ALL (including induction failure) or lymphoblastic non-hodgkin lymphoma. 3. No known contraindications to intended therapies. 4. Prior anthracycline exposure: Patients must have had less than 450 mg/m2 lifetime exposure of anthracycline chemotherapy. For patients whose cumulative dose is between 350-450 mg/m2, Zinecard is strongly recommended. 5. At least 3 months since the last treatment with a "VXLD" induction/re-induction type regimen (i.e., anthracycline, steroid, asparaginase and vincristine). 6. Eastern Cooperative Oncology Group (ECOG) performance status corresponding to 0, 1, or 2 and / or Karnofsky score above 50%. 7. Clinical laboratory values within the following parameters (repeat if more than 3 days before the first dose): 1. Albumin \> 2.7 g/dL 2. Total bilirubin ≤ 2.5 x upper limit of normal (ULN). 3. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 2.5 × ULN, 4. Creatinine clearance ≥ 50 mL/min; 5. White blood cell (WBC) count \< 50,000/µL before administration of pevonedistat on Cycle 1 Day 1. Note: Hydroxyurea or leukapheresis may be used to control the level of circulating leukemic blast cell counts. (if applicable) 8. Female patients who: * Are postmenopausal (see Appendix for definition) for at least 1 year before the screening visit, OR * Are surgically sterile, OR * If they are of childbearing potential: * Agree to practice 1 highly effective method and 1 additional effective (barrier) method of contraception (see Appendix), at the same time, from the time of signing the informed consent through 4 months after the last dose of study drug (female and male condoms should not be used together), or * Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[eg, calendar, ovulation, symptothermal, postovulation methods\] withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception.) 9. Male patients, even if surgically sterilized (ie, status postvasectomy), who: * Agree to practice effective barrier contraception during the entire study treatment period and through 4 months after the last dose of study drug (female and male condoms should not be used together), or * Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[eg, calendar, ovulation, symptothermal, postovulation methods for the female partner\] withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception.) 10. Voluntary written consent must be given before performance of any study related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care. 11. Patients must have recovered from the acute side effects of all prior anticancer therapy: * At least 1 week from prior cytotoxic chemotherapy. * At least 4 weeks from craniospinal irradiation * At least 4 months since hematopoietic stem cell transplant (HSCT) with no evidence of acute graft vs host disease (GVHD). Exclusion Criteria: 1. Treatment with any investigational products within 2 weeks before the first dose of any study drug. 2. Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of study procedures. 3. Active uncontrolled infection or severe infectious disease, defined as positive blood culture within 48 hours of study registration, need for supplemental oxygen or vasopressors within 48 hours of study entry. 4. Major surgery within 14 days before the first dose of any study drug or a scheduled surgery during study period. 5. Patients with nonmelanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone resection. 6. Patients with other malignancies that do not meet the exception in # 5 are excluded from participating in the trial. 7. Life-threatening illness unrelated to cancer. 8. Patients with uncontrolled coagulopathy or bleeding disorder, deemed not to be related to underlying disease. 9. Known human immunodeficiency virus (HIV) seropositive. 10. Known hepatitis B surface antigen seropositive or known or suspected active hepatitis C infection Note: Patients who have isolated positive hepatitis B core antibody (ie, in the setting of negative hepatitis B surface antigen and negative hepatitis B surface antibody) must have an undetectable hepatitis B viral load. Patients who have positive hepatitis C antibody may be included if they have an undetectable hepatitis C viral load. 11. Known hepatic cirrhosis or severe pre-existing hepatic impairment 12. Known cardiopulmonary disease defined as: * Unstable angina; * Congestive heart failure (New York Heart Association (NYHA) Class III or IV; see appendix); * Myocardial infarction (MI) within 6 months prior to first dose (patients who had ischemic heart disease such as a (ACS), MI, and/or revascularization greater than 6 months before screening and who are without cardiac symptoms may enroll); * Cardiomyopathy; * Clinically significant arrhythmia: 1. History of polymorphic ventricular fibrillation or torsade de pointes, 2. Permanent atrial fibrillation \[a fib\], defined as continuous a fib for ≥ 6 months, 3. Persistent a fib, defined as sustained a fib lasting \> 7 days and/or requiring cardioversion in the 4 weeks before screening, 4. Grade 3 a fib defined as symptomatic and incompletely controlled medically, or controlled with device (e.g. pacemaker), or ablation and 5. Patients with paroxysmal a fib or \< Gr 3 a fib for period of at least 6 months are permitted to enroll provided that their rate is controlled on a stable regimen. 6. Implantable cardioverter defibrillator; 7. Moderate to severe aortic and/or mitral stenosis or other valvulopathy (ongoing); 8. Clinically significant pulmonary hypertension requiring pharmacologic therapy. 13. Uncontrolled high blood pressure (ie, systolic blood pressure \> 180 mm Hg, diastolic blood pressure \> 95 mm Hg). 14. Prolonged rate corrected QT (QTc) interval ≥ 500 msec, calculated according to institutional guidelines. 15. Left ventricular ejection fraction (LVEF) \< 50% as assessed by echocardiogram or radionuclide angiography. 16. Known moderate to severe chronic obstructive pulmonary disease, interstitial lung disease, and pulmonary fibrosis. 17. Systemic antineoplastic therapy or radiotherapy for other malignant conditions within 14 days before the first dose of any study drug, except for hydroxyurea. 18. Female patients who are both lactating and breastfeeding or have a positive serum pregnancy test during the screening period or a positive urine pregnancy test on Day 1 before first dose of study drug. 19. Female patients who intend to donate eggs (ova) during the course of this study or 4 months after receiving their last dose of study drug(s). 20. Male patients who intend to donate sperm during the course of this study or 4 months after receiving their last dose of study drug(s). 21. No systemic corticosteroids allowed aside from dexamethasone treatment directed at leukemia. Systemic corticosteroids used for physiological replacement (e.g., adrenal insufficiency) are allowed. 22. Patients who are allergic to PEG-asparaginase or who cannot tolerate any asparaginase because of history of pancreatitis, will go on study without asparaginase. Substitution for Erwinaze is permitted for patients who had an allergic reaction to PEG-asparaginase. 23. Known intolerance to doxorubicin or vincristine. 24. Patients who have started protocol therapy prior to enrollment. Patient may still enroll if IT therapy was given within 72 hours of study enrollment as part of the diagnostic lumbar procedure.