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