Etoposide, Prednisone, Vincristine Sulfate, Cyclophosphamide, and Doxorubicin Hydrochloride With Asparaginase in Treating Patients With Acute Lymphoblastic Leukemia or Lymphoblastic Lymphoma

Inclusion Criteria: * Patients must have a confirmed diagnosis of either B- or T-cell acute lymphoblastic leukemia or lymphoblastic lymphoma that is either: * Arm A: Initially diagnosed at age 40 or later, OR * Arm B: Relapsed after or failed to respond to \>= 1 previous chemotherapy regimen * The regimen under study must constitute a reasonable therapeutic option * Presence of \>= 5% abnormal blasts in the bone marrow * Patients with prior allogeneic hematopoietic cell transplantation (HCT) must be at least 90 days post-HCT and must be on =\< 20 mg of prednisone (or equivalent dose of an alternative corticosteroid) for treatment/prevention of graft-vs-host disease * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN; unless attributable to Gilbert's disease or other causes of inherited indirect hyperbilirubinemia, at which point total bilirubin must be =\< 2.5 x ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 x institutional ULN * Note: Patients with liver test abnormalities attributable to hepatic involvement by ALL will be permitted if the total bilirubin is =\< 3.0 x ULN and ALT/AST are =\< 5.0 x ULN * Creatinine =\< 1.5 mg/dL; however, patients with a creatinine \> 1.5 mg/dL but with a calculated creatinine clearance of \> 60 ml/min, as measured by the Modification of Diet in Renal Disease (MDRD) equation, will be eligible * Measurement of left ventricular ejection fraction (LVEF) should be performed in patients with prior anthracycline exposure or known history of arrhythmia or structural heart disease; in these cases, LVEF must be \>= 40% * 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 * Per good clinical practice, any toxicity related to prior therapies that, in the opinion of the investigator, would potentially be worsened with DA-EPOCH-A +/- imatinib (imatinib mesylate) +/- rituximab, should be resolved to grade 1 or less * Eastern Cooperative Oncology Group (ECOG) performance status 0 to 2 * Women of childbearing potential must have a negative pregnancy test and must agree to the use of effective contraception while on treatment; men must also agree to the use of effective contraception while on treatment * Ability to give informed consent and comply with the protocol * Anticipated survival of at least 3 months Exclusion Criteria: * Patients with Burkitt lymphoma/leukemia * Patients must not have received chemotherapy within 14 days of enrollment, with the two following exceptions: * Routine systemic maintenance therapy (e.g., Abelson murine leukemia viral oncogene homolog 1 \[ABL\] kinase inhibitor, methotrexate, 6-mercaptopurine, vincristine, etc.) and intrathecal/intraventricular therapy * Systemic therapy for the acute management of hyperleukocytosis or acute symptoms (e.g., corticosteroids, cytarabine, etc.) * May not have prior malignancies unless the expected survival is at least 2 years * For patients with Philadelphia chromosome positive (Ph+) ALL, they must not have progressed within 3 months of receiving imatinib or have a documented ABL kinase mutation known to confer resistance to imatinib (e.g., T315I) * Patients with persistent grade 2 or higher peripheral sensory or motor neuropathy of any cause * Patients with isolated extramedullary disease or with parenchymal central nervous system (CNS) disease * Known hypersensitivity or intolerance to any of the agents under investigation * Human immunodeficiency virus (HIV) positive or evidence of infection with hepatitis B or C virus, as defined by any of the following criteria (if patients have not previously been tested for the following, these will be conducted during screening): * HIV antibody positive * Hepatitis B surface antigen or core antibody positive * Hepatitis C antibody positive * Other medical or psychiatric conditions that in the opinion of the investigator would preclude safe participation in the protocol * May not be pregnant or nursing