Sapanisertib in Treating Patients With Relapsed and/or Refractory Acute Lymphoblastic Leukemia

Inclusion Criteria: * World Health Organization (WHO)-defined acute lymphoblastic leukemia and either: * Relapsed after achieving remission * Refractory to therapy * Newly diagnosed and ineligible for intensive chemotherapy induction Note: patients with T lineage and B lineage ALL are eligible for this trial; likewise, patients with Philadelphia chromosome positive (Ph+) (as long as they are not candidate for other therapies for Ph+) and Ph- ALL are eligible * Bone marrow blasts of at least 10% * At least 4 weeks away from any previous antineoplastic or investigational agent; patients may receive hydroxyurea or glucocorticoids for suppression of leukocytosis, but these must be stopped at least 24 hours (h) prior to initiation of therapy * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Life expectancy of \> 2 months * Total bilirubin =\< 1.5 x institutional upper limit of normal * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal * Creatinine =\< 1.5 x institutional upper limit of normal * Fasting blood glucose (FBG) \< 130 mg/dL * Hemoglobin A1C (HbA1C) \< 7.0% * Relapse after SCT is allowed but no active graft-versus-host disease (GVHD) as per treating physician; also must not exceed the number of prior induction regimens listed above; SCT does not count as line of therapy * Negative seru…