Reduced Intensity Flu/Mel/TBI Conditioning for HAPLO HCT Patients With Hematologic Malignancies

Inclusion Criteria: * Age ≥ 55 years or HCT Co-Morbidity score (HCT-CI) \>/=3 * Lack of a suitable 8/8 HLA-matched sibling donor * Adequate performance status is defined as Karnofsky score ≥ 70% * Patients and selected donor must be HLA typed at high resolution using DNA based typing at the following HLA-loci: HLA-A, -B, -C and DRB1. Donors must be HLA-haploidentical relatives including, but not limited to, children, siblings, or parents, defined as having a shared HLA haplotype between donor and patient at HLA-A, -B, -C, and -DRB1. * Acute Myeloid Leukemia (AML): Must be in remission with morphology (\<5% blasts) * Acute Lymphoblastic Leukemia (ALL)/lymphoma second or greater complete remission (CR) first CR unable to tolerate consolidation chemotherapy due to chemotherapy-related toxicities, first CR high-risk ALL * Biphenotypic/Undifferentiated/Prolymphocytic Leukemias in first or subsequent CR * Myelodysplastic syndrome: any subtype including refractory anemia (RA) if severe pancytopenia or complex cytogenetics. Blasts must be less than 5%. If 5% of more requires chemotherapy for cytoreduction to \</=5% prior to transplantation. * Chronic Myelogenous leukemia in accelerated phase: patient must have failed at least two different Tyrosine Kinase Inhibitor (TKI)s, been intolerant to all TKIs, or have T315l mutation * Myeloproliferative neoplasms/myelofibrosis: Blasts must be less than 5%. If 5% or more requires chemotherapy for cytoreduction to \</=5% prior to transplantation * Relapsed large-cell lymphoma, mantle-cell lymphoma or Hodgkin lymphoma that is chemotherapy sensitive and has failed or ineligible for an autologous transplant * Burkitt's lymphoma in second CR or subsequent CR * Relapsed T-cell lymphoma that is chemotherapy sensitive in CR/Partial Response (PR) that has failed or ineligible for an autologous transplant * Natural killer cell malignancies * Relapsed chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL), marginal zone B-cell lymphoma, follicular lymphoma with any of the following: * Progressed within 12 months of achieving a partial or complete remission Patients who had remissions lasting up * Patients who had remission lasting \> 12 months are eligible after at least two prior therapies * Patients with primary, refractory disease. Bulky disease and an estimated tumor doubling time of less than one month require debulking therapy prior to transplant. * Lymphoplasmacytic lymphoma is eligible after initial therapy if chemotherapy sensitive * Adequate organ function as defined per protocol * Sexually active females of child bearing potential and males with partners of child bearing potential must agree to use adequate birth control during study treatment Exclusion Criteria: * Pregnant or breastfeeding * Untreated active infection * Active HIV infection * Prior allogenic transplant at any time prior or less than 6 months since prior autologous transplant (if applicable) * Active central nervous system malignancy * Favorable risk AML defined as per protocol * Active central nervous system malignancy * Favorable risk AML defined as having one of the following: * t(8,21) without cKIT mutation or evidence of immunophenotypic, cytogenetic or molecular minimal residual disease (MRD) * inv(16) or t(16;16) without cKIT mutation or evidence of MRD * Normal karyotype with mutated NPM1 but FLT3-ITD wild type without evidence of MRD * Normal karyatype with double mutated CEBPA without evidence of MRD