Trial Treating Relapsed Acute Lymphoblastic Leukemia With Venetoclax and Navitoclax

This is a phase I/II clinical trial evaluating the activity of combination chemotherapy with venetoclax and navitoclax in children with relapsed or refractory acute lymphoblastic leukemia or lymphoma (rALL) and assessing the combination dose of venetoclax combinations with either blinatumomab for CD19-positive patients or navitoclax and high-dose cytarabine for CD19-negative patients. Primary Objectives * To compare Minimal Residual Disease (MRD)-negative CR/CRi rate in children with relapsed or refractory acute lymphoblastic leukemia or lymphoma (rALL) following Block 1 therapy with venetoclax and navitoclax based reinduction to historical controls. * To identify the recommended phase 2 combination dose (RP2D) of venetoclax based consolidation in novel combinations with a) high-dose cytarabine and navitoclax or b) blinatumomab. Secondary Objectives * To estimate the tolerability and activity of venetoclax based consolidation in novel combinations with a) high-dose cytarabine and navitoclax or b) blinatumomab. * To describe event-free and overall survival in patients treated with this regimen. Exploratory Objectives * To evaluate MRD-negative CR/CRi rates in each prespecified groups: late first relapse B-ALL; early first relapse and second or greater relapse B-ALL; and relapsed T-ALL. * To identify drug sensitivity patterns in patient samples prior to and after receiving combination therapy and evaluate mechanisms of disease resistance/ escape. * To explore immune subsets during and after this regimen. * Evaluate response to therapy in rare relapse patient subsets. * Explore breakthrough infections in children and young adults with relapsed or refractory ALL

Inclusion Criteria: * Diagnosis: * Relapsed or refractory acute lymphoblastic leukemia or lymphoma with ≥1% bone marrow disease as measured by flow cytometry, PCR, or next generation sequencing. However, if an adequate bone marrow sample cannot be obtained, patients may be enrolled if there is unequivocal evidence of leukemia with ≥ 5% blasts in the peripheral blood. * Patients with 1-4.99% bone marrow involvement must have disease confirmed in one of the following ways: an alternative minimal residual disease assay (e.g. flow cytometry and PCR or NGS), cytogenetic abnormality consistent with patient's leukemia, FISH abnormality, or a second bone marrow with MRD ≥1% separated by 1-4 weeks. * Patients with ≥5% bone marrow disease by a single measurement as measured by flow cytometry, PCR, or next generation sequencing do not require a second confirmatory test. * Refractory disease is defined as residual leukemia ≥1% after at least 2 prior lines of frontline therapy with curative intent. * Patients in exploratory cohort I must have measurable extramedullary disease but may have \ 1.5x the ULN. Patients with a direct bilirubin ≥ 2 mg/dl may not enroll regardless of attribution. * Aspartate transaminase (AST) and alanine transaminase (ALT) \< 3.0 x the ULN unless increase is attributable to leukemic involvement. * Normal creatinine for age or a calculated creatinine clearance ≥ 60 mL/min/1.73 m\^2. * Left ventricular ejection fraction (LVEF) ≥ 40% or shortening fraction ≥ 25%. * Patients with a history of reduced LVEF which subsequently improved with medical management are eligible if they meet the criteria above. * Patients must have fully recovered from the acute effects of all prior therapy (defined as resolution of all such toxicities to ≤ Grade 2). * For patients with prior hematopoietic stem cell transplant (HSCT), at least 90 days must have elapsed since transplant, the patient cannot have evidence of active graft-versus-host disease (GVHD), and they must be off calcineurin inhibitors for ≥4 weeks, and off other immunosuppression for ≥2 weeks. * Patients with Down Syndrome/ germline Trisomy 21 are eligible for Block 1 and Block 2b therapies but are ineligible for Block 2a therapy. Patients with Down Syndrome and CD19-negative disease are off therapy after the response evaluation to Block 1. * Prior therapy * ≥14 days must have elapsed since the completion of cytotoxic therapy, with the exception of standard maintenance therapy (glucocorticoids, vincristine, methotrexate, 6-mercaptopurine), tyrosine kinase inhibitors, and steroids. * Cytoreduction with prednisone, methylprednisolone, or hydroxyurea for ≤ 120 hours (5 days) in patients with hyperleukocytosis or extramedullary disease compromising organ function can be initiated and continued until up to 24 hours prior to the start of protocol therapy. * At least 21 days must have elapsed since completion of therapy with a biologic agent excluding blinatumomab. For agents that have known adverse events occurring beyond 21 days after administration, this period prior to enrollment must be extended beyond the time during which adverse events are known to occur. At least 7 days must have elapsed since blinatumomab infusion and patients must have recovered from all toxicities as described above. * Intrathecal cytotoxic therapy: No waiting period is required for patients having received intrathecal cytarabine, methotrexate, and/or hydrocortisone. Intrathecal chemotherapy given at the time of diagnostic LP to evaluate for relapse prior to study enrollment is allowed. * Patient has not had prior exposure to navitoclax * Male or female participant of reproductive potential must agree to use appropriate methods of contraception for the duration of study treatment and for at least 30 days after last dose of protocol treatment. * Additional criteria for exploratory cohorts * Cohort I: Diagnosis of isolated extramedullary relapse as defined by bone marrow blasts of \