Fludarabine and Intermediate-dose TBI Followed by PTCy in Patients Undergoing Allo Transplant for Heme Malignancies

Inclusion Criteria: * Patients ages 18-65 years. * Patients with a diagnosis of one of the following hematologic malignancies: * Acute myeloid leukemia or chronic myeloid leukemia with no circulating blasts and less than 5% blasts in the bone marrow; * Myelodysplastic syndrome with less than 5% blasts in the bone marrow by IHC or flow cytometry whichever is highest; * Myeloproliferative neoplasms with less than 5% blast in the marrow and peripheral blood; * Acute lymphoblastic leukemia in CR (CIBMTR criteria); or Lymphoma in CR (CIBMTR criteria). * Patients who are eligible for allogeneic stem cell transplant per Transplant Program SOPs. * Patients with a Karnofsky performance status (KPS) of ≥60%. * Patients with adequate organ function defined by: * Cardiac: LVEF ≥50% * Pulmonary: DLCO ≥50% of predicted * Hepatic: Bilirubin ≤1.5x ULN, ALT/AST ≤2.5x ULN * Renal: Creatinine clearance ≥50 mL/min * All participants of reproductive potential must use effective contraception following allogeneic hematopoietic stem cell transplantation (allo-HSCT), in accordance with guidelines from the American Society for Transplantation and Cellular Therapy (ASTCT), the FDA, and other expert bodies. * For Male Participants: ○ Male participants must use effective contraception for at least 12 months after transplant, and longer if receiving immunosuppressive or cytotoxic medications. Chemotherapy and radiation can cause DNA damage to sperm, and even if fertility returns, mutations may persist for months. In cases where drugs such as mycophenolate mofetil (MMF) or lenalidomide are used, FDA guidance requires contraception for at least 90 days after discontinuation. Sperm cryopreservation should be offered prior to conditioning. Participants must avoid fathering a child during this time frame.15-17 * For Female Participants: * Female participants of childbearing potential are required to use highly effective contraception for a minimum of 12 to 24 months post-transplant, or longer if still receiving immunosuppressive or teratogenic therapy. For drugs such as MMF, sirolimus, or ruxolitinib, contraception must continue for 3 months after the last dose. * A woman is considered to be of childbearing potential if she is postmenarchal, has not reached a postmenopausal state (≥ 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus). The definition of childbearing potential may be adapted for alignment with local guidelines or requirements.15-17 * Patients with a suitable donor for allogeneic stem cell transplant defined by: * Matched sibling donors willing to donate mobilized peripheral blood (PBSC) or bone marrow (BM), meeting all institutional criteria for donation; * Unrelated donors at \>7/8 (i.e., mismatched at only one of the HLA-A, HLA-B, HLA-C, and HLA-DRB1 loci) willing to donate mobilized PBSC or BM, and medically eligible to donate cells according to National Marrow Donor Program criteria; or Related Haploidentical donors willing to donate PBSC or BM and meeting criteria for donation. * Patients who are able to comply with follow-up visits and treatment plans. * Patients who are able to give informed consent. Exclusion Criteria: * Hematopoietic cell transplantation comorbidity index above 3. * Patients with a Karnofsky performance status (KPS) of \<60%. * Patients with active infections or other contraindications for allogeneic stem cell transplant. * Patients who are unable or unwilling to give informed consent. * Patients who have received a prior allogeneic transplant. * Patients who are unable to comply with follow-up visits and treatment plans.