Inclusion Criteria:

        Age ≤30.99 years old

        Disease Status (Part A - Safety Phase)

          -  ALL in 1st, 2nd or 3rd relapse OR primary induction failure.

          -  AML in 1st ,2nd or 3rd relapse OR primary induction failure.

          -  T-or B -- Lymphoblastic Lymphoma (T-LBL, B-LBL); Diffuse Large B-cell Lymphoma (DLBCL)
             or Burkitt Lymphoma/Leukemia in 1st, 2nd or 3rd relapse OR primary induction failure.

        5.1.2.2 (Part B - Efficacy Phase)

          -  ALL in 2nd or 3rd relapse OR primary induction failure.

          -  AML in 2nd or 3rd relapse OR primary induction failure.

          -  T-or B -- Lymphoblastic Lymphoma (T-LBL, B-LBL); Diffuse Large B-cell Lymphoma (DLBCL)
             or Burkitt Lymphoma/Leukemia in 1st, 2nd or 3rd relapse OR primary induction failure.

        Adequate renal function defined as:

        - Normal Serum creatinine based on age or Creatinine clearance > 60 ml/min or >60
        ml/min/1.73 m2 or an equivalent radioisotope glomerular filtration rate (GFR) as determined
        by the institutional normal range.

        Adequate liver function defined as:

          -  Direct bilirubin < 1.5 upper limit of normal (ULN) for age, and SGOT (AST) or SGPT
             (ALT) <3 x ULN

        Adequate cardiac function defined as:

          -  Shortening fraction >27% by echocardiogram, or

          -  Ejection fraction of >50% by radionuclide angiogram or echocardiogram.

        Performance Status

          -  For patients age 1-16 years, Lansky score of ≥60.

          -  For patients > 16 years, Karnofsky score of ≥60.

        Negative urine pregnancy test for females of child bearing age.

        Prior Therapy - Patients are eligible if they have been treated with clofarabine,
        mitoxantrone, or a combination of both in the past. However, the maximal lifetime
        cumulative previous anthracycline dose should not exceed doxorubicin dose equivalent of 450
        mg/m2 (see Table 1). Patients who received more than one anthracycline prior to study entry
        should have each individual agent cumulative dose converted to doxorubicin equivalent and
        added together (eg, a patient who received cumulative dose of Daunorubicin at 200 mg/m2 and
        Mitoxantrone 48 mg/m2 has a total doxorubicin dose equivalent of 358.6 mg/m2 (200 mg/m2 x
        0.833 + 48 mg/m2 x 4).

        Table 1. Anthracycline Conversion Agent Conversion Factor to Doxorubicin Dose Doxorubicin
        Multiply total dose x 1 Daunorubicin Multiply total dose x 0.833 Idarubicin Multiply total
        dose x 5 Mitoxantrone Multiply total dose x 4

        Informed Consent

        - Patients or the patient's legally authorized guardian must be fully informed about their
        illness and the investigational nature of this protocol (including foreseeable risks and
        possible side effects), and must sign an informed consent in accordance with the
        institutional policies approved by the U.S. Department of Health and Human Services.

        Exclusion Criteria:

        Patients with prior myeloablative allogeneic stem cell transplantation <3 months prior to
        proposed enrollment on study and/or ≥Grade II active acute GVHD or extensive chronic GVHD.

        Females who are pregnant (positive HCG) or lactating.

        Karnofsky <60% or Lansky <60% if less than 16 years of age.

        Age >30.99 years of age.

        Patients with active CNS disease.

        Any patient with uncontrolled infection prior to study entry.

        Patients with Down syndrome are excluded.