T- cell acute lymphoblastic leukemia (T-ALL) or T-cell lymphoblastic lymphoma (T-LLy) has an increase in proteins in a specific pathway called the mTOR pathway within the cancer cells. In cancer cells it can encourage untimely cell growth, cell production, and cell survival. Everolimus is an inhibitor of the mTOR pathway and can decrease the growth and survival of cancer cells. It also prevents communication within cells and stops proteins from being made that may contribute to leukemia. The main purpose of the study is to find the maximum tolerated dose of everolimus when used together with standard chemotherapy.