Obatoclax Mesylate, Vincristine Sulfate, Doxorubicin Hydrochloride, and Dexrazoxane Hydrochloride in Treating Young Patients With Relapsed or Refractory Solid Tumors, Lymphoma, or Leukemia

Inclusion Criteria: * Stratum 1 (solid tumors, including lymphomas): patients must have had histologic verification of malignancy at original diagnosis or relapse; patients with recurrent or refractory solid tumors are eligible, excluding primary central nervous system (CNS) tumors or patients with known CNS metastases * Stratum 2 (mixed-lineage leukemia \[MLL\] + leukemia): patients with recurrent or refractory MLL+ leukemia are eligible excluding those patients with symptomatic CNS leukemia, CNS chloromas, or leptomeningeal leukemic involvement * Stratum 3 (other leukemias): patients with non-MLL+ recurrent or refractory leukemia (acute lymphoblastic leukemia \[ALL\], acute myeloid leukemia \[AML\] or chronic myeloid leukemia \[CML\] in blast crisis) are eligible excluding those patients with symptomatic CNS leukemia, CNS chloromas, or leptomeningeal leukemic involvement * Stratum 1: patients must have either measurable or evaluable disease * Strata 2 and 3: patients with leukemia must have a \> 25% blasts on bone marrow aspirate to be eligible * Patient's current disease state must be one for which there is no known curative therapy or therapy proven to prolong survival with an acceptable quality of life * Karnofsky \>= 50% for patients \> 16 years of age and Lansky \>= 50 for patients =\< 16 years of age * Patients must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study * Myelosuppressive chemotherapy: must not have received within 3 weeks of enrollment onto this study (6 weeks if prior nitrosourea); hydroxyurea may be administered prior to study enrollment; in such cases at least 24 hours must have elapsed between the last dose of hydroxyurea and the first dose of obatoclax * Hematopoietic growth factors: at least 7 days since the completion of therapy with a growth factor * Biologic (anti-neoplastic agent): at least 7 days since the completion of therapy with a biologic agent; for agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur; the duration of this interval must be discussed with the study chair * Immunotherapy: at least 6 weeks since the completion of any type of immunotherapy, e.g. tumor vaccines * Monoclonal antibodies: at least 3 half-lives since prior therapy that includes a monoclonal antibody * Radiation therapy (XRT): \>= 2 weeks (wks) for local palliative XRT (small port); \>= 6 months must have elapsed if prior total-body irradiation (TBI), craniospinal XRT or if \>= 50% radiation of pelvis; \>= 6 wks must have elapsed if other substantial bone marrow (BM) radiation * Stem cell transplant or rescue without TBI: no evidence of active graft vs. host disease and \>= 3 months must have elapsed since transplant * STRATUM 1: Peripheral absolute neutrophil count (ANC) \>= 1000/mm\^3 * STRATUS 1: Platelet count \>= 100,000/mm\^3 (transfusion independent, defined as not receiving platelet transfusions within a 7 day period prior to enrollment) * STRATUM 1: Hemoglobin \>= 8.0 g/dL (may receive red blood cell \[RBC\] transfusions) * STRATA 2 and 3: Platelet count \>= 20,000/mm\^3 (may receive platelet transfusions) * STRATA 2 and 3: Hemoglobin \>= 8.0 g/dL (may receive RBC transfusions) * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70ml/min/1.73 m\^2 OR a serum creatinine based on age/gender as follows: * 0.5 mg/dL (6 months to \< 1 year of age) * 0.6 mg/dL (1 to \< 2 years of age) * 0.8 mg/dL (2 to \< 6 years of age) * 1 mg/dL (6 to \< 10 years of age) * 1.2 mg/dL (10 to \< 13 years of age) * 1.5 mg/dL (male) or 1.4 mg/dL (female) (13 to \< 16 years of age) * 1.7 mg/dL (male) or 1.4 mg/dL (female) (\>= 16 years of age) * Bilirubin (sum of conjugated + unconjugated) \>= 1.5 x upper limit of normal (ULN) for age * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) \>= 110 U/L; for the purpose of this study, the ULN for SGPT is 45 U/L * Serum albumin \>= 2 g/dL * Shortening fraction of \>= 27% by echocardiogram, or ejection fraction of \>= 50% by gated radionuclide study * Stable neurological examination for at least 2 weeks prior to study enrollment; no known \> grade 2 unresolved neurological toxicities * All patients and/or their parents or legal guardians must sign a written informed consent; assent, when appropriate, will be obtained according to institutional guidelines Exclusion Criteria: * Pregnant or breast-feeding women will not be entered on this study; pregnancy tests must be obtained in girls who are post-menarchal; males or females of reproductive potential may not participate unless they have agreed to use an effective contraceptive method * Growth factors that support platelet or white cell number or function must not have been administered within the 7 days prior to enrollment * Patients requiring corticosteroids who have not been on a stable or decreasing dose of corticosteroid for the prior 7 days * Patients who are currently receiving another investigational drug are not eligible * Patients who are currently receiving other anticancer agents, with the exception of hydroxyurea, are not eligible; patients with leukemia may receive intrathecal therapy as outlined * Any anti-convulsant medications * Patients who have an uncontrolled infection are not eligible * Patients who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study are not eligible * Patients with a total lifetime cumulative anthracycline dose \> 750 mg/m2 (25 mg/kg if \< 1 year) doxorubicin or equivalent at the time of enrollment are not eligible