The purpose of this study is to determine the safety and effectiveness of an experimental form of therapy, known as BEAM-201. BEAM-201 uses immune cells, called T cells, that are genetically changed to identify cancer cells. In this study, T cells are collected from a healthy human donor and have been modified in a laboratory. If the genetically changed T cells recognize and attach to cancer cells, they may have the ability to kill those cancer cells. The U.S. Food and Drug Administration (FDA) allows BEAM-201 to be used in research. Patients with T-cell Acute Lymphoblastic Leukemia (T-ALL) or T-cell Lymphoblastic Lymphoma (L-LL), where the disease has come back (relapsed) or has not responded to treatment (refractory) may be eligible for the study.