Intravenous Ixazomib in Pediatric Participants With Relapsed or Refractory Acute Lymphoblastic Leukemia (ALL) or Lymphoblastic Lymphoma (LLy)

Inclusion Criteria: 1. Diagnosis of relapsed/refractory ALL with or without extramedullary disease, including central nervous system (CNS)2 (\<5 white blood cell \[WBC\]/mcL\] in the cerebrospinal fluid \[CSF\] with blasts) and CNS3 (\>=5 WBC/mcL in the CSF with blasts), or relapsed/refractory LLy. Participants with mixed-phenotype ALL or mature (Burkitt-like) leukemia are excluded. 2. Relapsed/refractory ALL must have \>=5% blasts in the bone marrow by morphology. 3. Relapsed/refractory LLy participants must have measurable disease documented by clinical, radiologic, and histologic criteria. 4. A Karnofsky performance status of \>=50% (for participants aged \>16 years) and a Lansky performance status of \>=50% (for participants aged \<=16 years). 5. Adequate organ function. 6. Failure of 1 or more therapeutic attempts. 7. Full recovery from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy before entering this study, as follows: * Cytoreduction with hydroxyurea: Hydroxyurea can be initiated and continued for up to 24 hours before the start of protocol therapy. * Cytotoxic therapy: At least 14 days must have elapsed since the completion of the last dose of chemotherapy, except intrathecal (IT) chemotherapy and/or maintenance therapy, such as vincristine (VCR), mercaptopurine, methotrexate, or glucocorticoids. There is no waiting period for those relapsing on maintenance therapy. * Hematopoietic stem cell transplantation (HSCT): Participants who have relapsed after HSCT are eligible, provided they have no evidence of acute or chronic graft-versus-host disease (GVHD), are not receiving GVHD prophylaxis or treatment, and are at least 90 days posttransplant at the time of enrollment. * Hematopoietic growth factors: At least 7 days must have elapsed since the completion of therapy with granulocyte colony-stimulating factor (G-CSF) or other growth factor at the time of enrollment. At least 14 days must have elapsed since the completion of therapy with pegfilgrastim. * Biologic (antineoplastic agent): At least 7 days must have elapsed since the last dose of a biologic agent. For agents that have known adverse events (AEs) occurring beyond 7 days after the end of administration, this period must be extended beyond the time during which AE are known to occur. The duration of this interval must be approved by the project clinician (or designee). * Monoclonal antibodies: At least 3 half-lives must have elapsed after the last dose of an administered monoclonal antibody. * Immunotherapy: At least 30 days must have elapsed after the completion of any type of immunotherapy (example, tumor vaccines, chimeric antigen receptor T-cells). * Photon radiotherapy (XRT): Craniospinal XRT is prohibited during protocol therapy. No washout period is necessary for radiation given to any extramedullary site other than the CNS; \>=90 days must have elapsed if prior total body irradiation or craniospinal XRT was given. * Anthracyclines: Participants must have had a lifetime exposure of \<400 mg/m\^2 of doxorubicin equivalents of anthracyclines. * Proteasome inhibitors: Participants with a prior exposure to proteasome inhibitor (PIs) (example, bortezomib, carfilzomib) are eligible as long as the participant demonstrated at least a partial response to chemotherapy with a PI. Exclusion criteria: 1. ALL participants: have isolated extramedullary disease, including CNS or testicular disease. 2. Have Grade \>=2 peripheral sensory or motor neuropathy, defined by the Modified "Balis" Pediatric Scale of Pediatric Neuropathies, at the time of enrollment. 3. Have a planned administration of chemotherapy, radiation therapy, or immunotherapy, other than the study drugs used for this protocol. 4. Have deoxyribonucleic acid fragility syndromes (example, Fanconi anemia, Bloom syndrome). 5. Have Down syndrome. 6. Are receiving cyclosporine, tacrolimus, or other agents to prevent graft-versus host disease (GVHD) after HSCT. 7. Have Philadelphia chromosome (Ph)-positive ALL or Ph-like ALL and are currently receiving tyrosine kinase inhibitor therapy. 8. Are receiving systemic treatment with strong inducers of cytochrome P450 3A (CYP3A)(example,rifampin, rifapentine, rifabutin, carbamazepine, phenytoin, phenobarbital, St. John's wort) within 14 days before study enrollment. 9. Are receiving systemic treatment with strong CYP3A inhibitors within 14 days before study enrollment. 10. Are receiving systemic treatment with inhibitors or inducers of P-glycoprotein (P-gp) within 14 days before study enrollment.