Study of the Tocilizumab Optimization Timing for CART19 Associated Cytokine Release Syndrome

Inclusion Criteria: 1. Signed informed consent form must be obtained prior to any study procedure. Labs, marrows or other procedures obtained during routine clinical care may be used for eligibility if obtained within the protocol required windows. 2. Relapsed or refractory B-cell ALL: 1. 2nd or greater marrow relapse OR 2. CNS relapse OR 3. Any relapse after allogeneic hematopoietic stem cell (SCT) transplant and ≥ 4 months from SCT at enrollment OR 4. Any relapse after CAR-modified T cell therapy OR 5. Refractory disease defined as having not achieved an MRD-negative CR after ≥ 2 chemotherapy regimens/cycles (1 cycle for relapsed patients) OR 6. Patients with Ph+ ALL are eligible if they are intolerant to or have failed tyrosine kinase inhibitor therapy OR 7. Ineligible for allogeneic SCT because of: * Comorbid disease * Other contraindications to allogeneic SCT conditioning regimen * Lack of suitable donor * Prior SCT * Declines allogeneic SCT as the therapeutic option after documented discussion, with expected outcomes, about the role of SCT with a bone marrow transplant (BMT) physician not part of the study team 8. Patients with B lymphoblastic lymphoma will be eligible if they meet one of the above criteria OR: * 2nd or greater relapse OR * Refractory disease defined as having not achieved CR with frontline therapy or after 1 cycle of reinduction therapy for relapsed patients 9. Patients with prior or current history of CNS3 disease will be eligible if CNS disease is responsive to therapy (at infusion, must meet criteria in Section 5.3) 3. Documentation of CD19 tumor expression in bone marrow, peripheral blood, CSF, or tumor tissue by flow cytometry at relapse (or a recent sample in the case of refractory disease). If the patient has received CD19-directed therapy (i.e. blinatumomab), then the flow cytometry should be obtained after this therapy to show CD19 expression. 4. Adequate organ function defined as: 1. A serum creatinine based on age/gender as follows: Maximum Serum Creatinine (mg/dL) Age Male Female * 1 to \< 2 years 0.6 0.6 * 2 to \< 6 years 0.8 0.8 * 6 to \< 10 years 1.0 1.0 * 10 to \< 13 years 1.2 1.2 * 13 to \< 16 years 1.5 1.4 * ≥ 16 years 1.7 1.4 2. ALT ≤500 U/L 3. Bilirubin ≤2.0 mg/dl 4. Must have a minimum level of pulmonary reserve defined as ≤ Grade 1 dyspnea, pulse oximetry \> 92% on room air; DLCO ≥ 40% (corrected for anemia) if PFTs are clinically appropriate as determined by the treating investigator 5. Left Ventricular Shortening Fraction (LVSF) ≥ 28% or Ejection Fraction (LVEF) ≥ 40% confirmed by ECHO, or adequate ventricular function documented by a scan or a cardiologist. 5. Evidence of disease by standard morphologic or MRD criteria. A clinical marrow or tissue biopsy showing disease may be performed at enrollment or within 12 weeks of enrollment. Presence of marrow disease not required for CNS disease or lymphoblastic lymphoma patients. 6. Age 1-29 years. Patients ages 24-29 years are eligible if their original leukemia diagnosis was prior to age 21. 7. Adequate performance status (Lansky or Karnofsky score ≥50). 8. Subjects of reproductive potential must agree to use acceptable birth control methods, as described in protocol Section 4.3. Exclusion Criteria: 1. Active hepatitis B or active hepatitis C. 2. HIV Infection. 3. Active acute or chronic graft-versus-host disease (GVHD) requiring systemic therapy. 5\. CNS3 disease that is progressive on therapy, or with CNS parenchymal lesions that might increase the risk of CNS toxicity. 6\. Pregnant or nursing (lactating) women. 8. Uncontrolled active infection.