MK2206 in Treating Younger Patients With Recurrent or Refractory Solid Tumors or Leukemia

Inclusion Criteria: * Patients must have a body surface area \> 0.5 m\^2 when enrolling on dose levels 0 or 1 of the every other day schedule; no body surface area (BSA) restrictions apply to patients enrolling on higher dose levels; no BSA restrictions apply to patients enrolling on any dose level of the weekly schedule. * Diagnosis: * Part A (both schedules): Patients must have a diagnosis of recurrent or refractory solid tumors, including central nervous system (CNS) tumors or lymphoma; patients must have had histologic verification of malignancy at original diagnosis or relapse except in patients with intrinsic brain stem tumors, optic pathway gliomas, or patients with pineal tumors and elevations of cerebrospinal fluid (CSF) or serum tumor markers including alpha-fetoprotein or beta-human chorionic gonadotropin (HCG) * Part B (both schedules): Patients must have a diagnosis of recurrent or refractory leukemia * Disease status: * Solid tumors: Patients must have either measurable or evaluable disease * Leukemia: Patients must have \>= 5% blasts in the bone marrow; active extramedullary disease (except for leptomeningeal disease) may also be present * 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; note: neurologic deficits in patients with CNS tum…