Anti-CD7 CAR-T Cells in Relapsed/Refractory T-Cell Acute Lymphoblastic Leukemia or Lymphoma

Patients must meet all the following criteria to be eligible for enrollment into the study: 1. Patients (ages ≥ 18 years) or parent/legal guardians (for patients ages \< 18 years) must provide signed, written informed consent according to local IRB and institutional requirements. 2. Ages 0 to 29 years. 3. T-ALL/T-LLy in second or greater relapse, first relapse post-transplant, or chemotherapy-refractory disease. Specifically: 1. Second or greater relapse or post-transplant relapse, defined as: * BM with ≥ 5% lymphoblasts by morphologic assessment or evidence of extramedullary disease after second documented CR; OR * Flow cytometric confirmation of relapsed T-ALL of at least 0.1% after second CR documented to have been MRD negative \< 0.1%; OR * Any detectable relapsed disease post-allogeneic HSCT with flow cytometric confirmation of T-ALL of at least 0.1%; OR * Biopsy confirmed evidence of relapsed T-LLy after second CR; OR * Any detectable disease post-allogeneic transplant with biopsy confirmed evidence of T-LLy 2. Refractory disease, defined as: * Primary refractory T-ALL or T-LLy, defined as failure to achieve CR after induction chemotherapy, per investigator assessment and based on biopsy-or MRD-confirmed evidence of residual T-ALL or T-LLy; OR * Relapsed, refractory disease, defined as \> 0.1 % MRD or morphologic evidence of disease or evidence of residual T-LLy after 1 course of re-induction chemotherapy for patients who have relapsed after previously achieving a CR NOTE: Patients with mixed phenotype acute leukemia with T cell dominant phenotype may be enrolled if the aforementioned criteria are met. 4. Documentation of CD7 expression on leukemic or T-LLy blasts (defined as at least 90% of blasts positive for CD7 by flow cytometry or immunohistochemistry). 5. Patients with prior or current history of CNS3 disease will be eligible if CNS disease is responsive to therapy 6. Eligible for myeloablative conditioning for and allogeneic HSCT based on the investigator's assessment with an available donor identified by a FACT accredited transplant center. 7. Lansky Performance Status (ages \< 16 years at time of consent) or Karnofsky Performance Status (KPS) (ages ≥ 16 years at time of consent) score of ≥ 50. 8. Patients of childbearing potential must have a negative urine or serum pregnancy test at screening. 9. Adequate organ function defined as: 1. Adequate Serum creatinine based on age/gender 2. ALT ≤ 5x ULN in the absence of ALL infiltration of the liver 3. Bilirubin ≤ 3 × ULN for age Note: ALT and/or bilirubin results that exceed this range are acceptable if, in the opinion of the physician-investigator (or as confirmed by liver biopsy), the abnormalities are directly related to ALL infiltration of the liver. 4. Must have a minimum level of pulmonary reserve defined as ≤ Grade 1 dyspnea and \<Grade 3 hypoxia; DLCO ≥40% (corrected for anemia if necessary) if PFTs are clinically appropriate as determined by the investigator. 5. Cardiac echocardiography (ECHO) with left ventricular shortening fraction (LVSF) ≥ 30% or left ventricular ejection fraction (LVEF) ≥ 50%. In cases where quantitative assessment of LVSF/LVEF is not possible, a statement by the cardiologist that the ECHO shows qualitatively normal ventricular function will suffice 10. Patients who are sexually active and of reproductive potential must agree to use an acceptable form of highly effective contraception from consent to 12 months after BEAM 201 infusion. 4.2 Exclusion Criteria Patients who meet any of the following criteria will be disqualified from entering the study: 1. Active hepatitis B or active hepatitis C 2. Active HTLV infection 3. HIV infection 4. Uncontrolled, active bacterial, viral, or fungal infection. 5. CNS disease that is progressive on therapy, or with CNS parenchymal lesions that might increase the risk of CNS toxicity. 6. Clinically active CNS dysfunction or known history of irreversible central neurological toxicity related to prior antileukemic therapy. 7. Receipt of prior CD7 targeted therapy. 8. Radiation therapy within 2 weeks prior to completion of screening, other than prophylaxis for CNS disease. 9. Acute GVHD that is grade ≥ 2 and requiring systemic immunosuppression (corticosteroids), or chronic GVHD that is mild, moderate, or severe and requiring systemic immunosuppression (corticosteroids). Grade 1 acute GVHD not requiring immunosuppression is allowable. 10. Undergone HSCT within 90 days prior to completion of screening (or donor leukocyte infusion, if received within 30 days prior to completion of screening). 11. Any other condition that would make the patient ineligible for HSCT as determined by the investigator. 12. Known primary immunodeficiency or BM failure syndrome. 13. Atrial fibrillation/flutter (not including isolated episodes that responded to medical management) 14. Clinically significant pericardial effusion 15. Myocardial infarction within the last 12 months 16. QT interval corrected for heart rate \> 480 msec 17. Cardiac dysfunction NYHA (New York Heart Association) III or IV 18. Patients with an autoimmune disorder requiring systemic immunosuppressive therapy that cannot be safely withheld for 3 months. Concurrent use of systemic corticosteroids for diagnoses unrelated to T-ALL/T-LLy is prohibited, with exception of physiologic corticosteroid replacement therapy treatment for adrenal insufficiency. 19. Pregnant or breastfeeding