‣ Patients must meet all the following criteria to be eligible for enrollment into the study:

• 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.

• Ages 0 to 29 years.

• T-ALL/T-LLy in second or greater relapse, first relapse post-transplant, or chemotherapy-refractory disease. Specifically:

∙ 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

‣ 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.

• 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).

• Patients with prior or current history of CNS3 disease will be eligible if CNS disease is responsive to therapy

• 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.

• 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.

• Patients of childbearing potential must have a negative urine or serum pregnancy test at screening.

• Adequate organ function defined as:

∙ Adequate Serum creatinine based on age/gender

‣ ALT ≤ 5x ULN in the absence of ALL infiltration of the liver

‣ 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.

‣ Must have a minimum level of pulmonary reserve defined as ≤ Grade 1 dyspnea and \<Grade 3 hypoxia; DLCO ≥40% (corrected for anemia) if PFTs are clinically appropriate as determined by the investigator.

‣ 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

⁃ 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.