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