Etoposide, Prednisone, Vincristine, Cyclophosphamide, and Doxorubicin (DA-EPOCH) With or Without Rituximab Plus Recombinant Erwinia Asparaginase (JZP458) for the Treatment of Newly Diagnosed Ph Negative B-Acute Lymphoblastic Leukemia or T Acute Lymphoblastic Leukemia

Inclusion Criteria: * Adults (age 18 years and older) with newly-diagnosed Ph- B-ALL or T-ALL * In the opinion of the treating investigator, patients must be an unsuitable candidate for a pediatric-inspired regimen, reasons for which may include (but not be limited to) older age (e.g., ≥ 40 years), practical/logistical barriers to or toxicity concerns from administration of a pediatric-inspired regimen * Marrow or blood involvement by ALL detectable by multi-parameter flow cytometry (MFC) * Eastern Cooperative Oncology Group (ECOG) performance status 0 to 2. (Performance status of 3 will be allowed if poor performance status is thought to be directly secondary to ALL.) * Total bilirubin ≤ 2.0 x upper limit of normal (ULN) (unless attributed to Gilbert's disease or other causes of inherited indirect hyperbilirubinemia, at which point total bilirubin must be ≤ 4.0 x ULN) (Note: Patients with liver test abnormalities attributable to hepatic involvement by ALL will be permitted if the total bilirubin is ≤ 5.0 x ULN and alanine aminotransferase \[ALT\]/aspartate aminotransferase \[AST\] are ≤ 8.0 x ULN.) * AST (serum glutamic oxaloacetic transaminase \[SGOT\])/ALT (serum glutamic pyruvic transaminase \[SGPT\]) ≤ 5.0 x institutional ULN. (Note: Patients with liver test abnormalities attributable to hepatic involvement by ALL will be permitted if the total bilirubin is ≤ 5.0 x ULN and ALT/AST are ≤ 8.0 x ULN.) * Calculated creatinine clearance of ≥ 60 ml/min/1.73 m\^2, as measured by the Modification of Diet in Renal Disease (MDRD) equation, will be eligible * As patients with ALL frequently have cytopenias, no hematologic parameters will be required for enrollment or to receive the first cycle of treatment. However, adequate recovery of blood counts will be required to receive subsequent cycles * Ability to give informed consent and comply with the protocol * Anticipated survival of at least 3 months, independent of ALL * Female subjects of childbearing potential should use effective non-hormonal contraceptive methods during treatment with JZP458 and for 3 months after the last dose of study drug. Male subjects with female partners of childbearing potential must agree to use an effective method of birth control from the time of signing the consent form until at least 3 months after the last dose of study drug Exclusion Criteria: * Prior systemic therapy for ALL except to control acute symptoms and/or leukocytosis (e.g., corticosteroids, cytarabine, etc.). Cytarabine 500 mg/m\^2 per dose up to 2 doses and/or the equivalent of prednisone 50 mg/m\^2/day for up to 2 days are permitted * Burkitt lymphoma/leukemia * Isolated extramedullary or known parenchymal central nervous system (CNS) disease * Known hypersensitivity or intolerance to any of the agents under investigation * Known history of grade 3+ pancreatitis or chronic pancreatic insufficiency * Known active chronic liver disease including, but not limited to, non-alcoholic steatohepatitis, cirrhosis, or non-alcoholic fatty liver disease * Other medical or psychiatric conditions that in the opinion of the investigator would preclude safe participation in the protocol * Pregnant or nursing * Pregnancy test is only required in women, unless they are highly unlikely to conceive (defined as \[1\] surgically sterilized, or \[2\] postmenopausal \[i.e., a woman who is \> 50 years old or who has not had menses for ≥ 1 year\], or \[3\] not heterosexually active)