Inclusion Criteria:

- Diagnosis:

- Patients must have 2nd or greater relapse of pre-B ALL, T-cell ALL,
lymphoblastic lymphoma, or peripheral T-cell lymphoma; patients may not have
refractory disease

- Patients with ALL, lymphoblastic lymphoma or peripheral T-cell lymphoma
refractory to first relapse therapy are eligible for enrollment

- Patients with leukemia must have had histologic verification of the malignancy
at the most recent relapse, including immunophenotyping to confirm diagnosis

- Disease Status:

- Leukemia: Patients with leukemia must have an M3 marrow with or without
extramedullary site of relapse OR an M2 bone marrow with an extramedullary site
of relapse; patients with CNS 3 status are not eligible for enrollment

- Lymphoma: Patients with non-Hodgkin lymphoma must have either measurable or
evaluable disease

- 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 who are unable to walk because of paralysis, but who are up in
a wheelchair, will be considered ambulatory for the purpose of assessing the
performance score

- Prior Therapy:

- Patients must have fully recovered from the acute toxic effects of all prior
anti-cancer chemotherapy, defined as resolution of all such toxicities to =<
Grade 2 or per the inclusion/exclusion criteria

- Myelosuppressive chemotherapy:

- Patients with leukemia or lymphoma who relapse while receiving standard
maintenance chemotherapy with steroid, vincristine pulses and oral
outpatient chemotherapy will not be required to have a waiting period
before enrollment onto this study

- Patients who relapse while they are not receiving standard maintenance
therapy, must have fully recovered from all acute toxic effects of prior
therapy; at least 14 days must have elapsed after the completion of
cytotoxic therapy, with the exception of hydroxyurea

- Note: Cytoreduction with hydroxyurea in patients can be initiated and
continued for up to 24 hours prior to the start of protocol therapy

- Hematopoietic growth factors: At least 14 days after the last dose of a
long-acting growth factor (e.g. Neulasta) or 7 days for short-acting growth
factor; 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

- Biologic (anti-neoplastic agent): At least 7 days after the last dose of 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 42 days after the completion of any type of
immunotherapy, e.g. tumor vaccines

- Monoclonal antibodies: At least 3 half-lives of the antibody after the last dose
of a monoclonal antibody with the exception of blinatumomab; patients must have
been off blinatumomab infusion for at least 7 days and all drug-related toxicity
must have resolved to Grade 1 or lower as outline in the inclusion and exclusion
criteria

- XRT: At least 14 days after local palliative XRT (small port); At least 84 days
must have elapsed if prior TBI, craniospinal XRT or if >= 50% radiation of
pelvis; At least 42 days must have elapsed if other substantial BM radiation

- Stem Cell Infusion: No evidence of active graft vs. host disease and at least 84
days must have elapsed after transplant or stem cell infusion

- Study specific limitations on prior therapy: Patient may not have received prior
therapy with an mTOR inhibitor

- Platelet count >= 20,000/mm^3 (may receive platelet transfusions) to initiate therapy

- Patients must not be known to be refractory to red cell or platelet transfusion

- Creatinine clearance or radioisotope GFR >= 70ml/min/1.73 m^2

- Bilirubin (sum of conjugated + unconjugated) =< 1.5 x upper limit of normal (ULN) for
age

- SGPT (ALT) =< 225 U/L; for the purpose of this study, the ULN for SGPT is 45 U/L

- GGT =< ULN for age

- Serum albumin >= 2 g/dL

- Shortening fraction of >= 27% by echocardiogram, or ejection fraction of >= 50% by
gated radionuclide study

- Pulse oximetry > 94% on room air

- Baseline chest x-ray; patients with active infectious disease or pneumonitis are not
eligible

- Serum triglyceride level =< 300 mg/dL and serum cholesterol level =< 300 mg/dL

- Random or fasting blood glucose within the upper normal limits for age; iIf the
initial blood glucose is a random sample that is above the upper normal limits, then
a follow-up fasting blood glucose can be obtained and must be within the upper normal
limits for age

- All patients and/or their parents or legally authorized representatives must sign a
written informed consent; assent, when appropriate, will be obtained according to
institutional guidelines

- Patients who are currently receiving other anticancer agents are not eligible (except
patients receiving hydroxyurea, which may be continued until 24 hours prior to start
of protocol therapy)

Exclusion Criteria:

- Pregnant or breast-feeding women will not be entered on this study

- Patients receiving stable or decreasing doses of corticosteroids for =< 7 days prior
to enrollment, or who are receiving increasing doses of corticosteroids, are not
eligible for enrollment; the exception to this is pulsed steroids used for
maintenance chemotherapy

- Patients who are currently receiving another investigational drug are not eligible

- Patients who are receiving cyclosporine, tacrolimus or other agents to prevent
graft-versus-host disease post bone marrow transplant are not eligible for this trial

- Patients who cannot receive asparginase are not permitted on trial; substitution with
Asparaginase Erwinia Chrysanthemi is acceptable

- Cumulative prior anthracycline exposure must not exceed 400 mg/m^2 (each 10 mg/m^2 of
idarubicin or mitoxantrone should be calculated as the isotoxic equivalent of 30
mg/m2 of daunorubicin or doxorubicin)

- Patients who are currently receiving therapeutic anticoagulants (including aspirin,
low molecular weight heparin, and others) are not eligible

- Patients who are currently receiving ACE inhibitors are not eligible due to the
development of angioneurotic edema-type reactions in some subjects who received
concurrent treatment with temsirolimus + ACE inhibitors

- Enzyme-Inducing anti-convulsants: Patients who are currently receiving
enzyme-inducing anti-convulsants (i.e., phenytoin, phenobarbitol, or carbamazepine)
are not eligible

- Patients with CNS 3 status at enrollment are not eligible

- Patients must have no pre-existing Grade 1 or higher ulcerations, fistulas, mucosal
lesions, or skin barrier breakdown

- Patients who have an uncontrolled infection are not eligible

- Patients with known optic nerve and/or retinal involvement (because it may not be
possible to safely delay irradiation) are not eligible; patients presenting with
visual disturbances by history or physical exam should have an ophthalmological exam
and MRI within 14 days prior to enrollment to determine whether there is optic nerve
or retinal involvement

- Patients with known Down syndrome, Fanconi anemia, Kostmann syndrome, Shwachman
syndrome or any other known bone marrow failure syndrome are not eligible

- Patients who have received a prior solid organ transplantation 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