Reduced Intensity Conditioning (RIC) Regimen and Post-transplant Cyclophosphamide in Haploidentical Bone Marrow Transplantation in in Patients With Poor Prognosis Lymphomas

* Signed and dated IEC-approved informed consent * Age ≥ 18-70 years old. * Performance Status Karnofsky ≥ 80% (see appendix B) * HLA typing will be performed at high resolution (allele level) for the HLA-A, HLA -B, HLA Cw, HLA-DRB1, and HLA-DQB1 loci. A minimum match of 5/10 is required. An unrelated donor search is not required for a patient to be eligible for this protocol if the clinical situation dictates an urgent transplant. * The donor and recipient must be identical, as determined by high resolution typing, at least one allele of each of the following genetic loci: HLA-A, HLA-B, HLA-Cw, HLA-DRB1, and HLA-DQB1. * Patients with lymphoma (any histology) relapsed after high dose chemotherapy and in partial remission, complete remission or stable disease after the last CT line. 1. Hodgkin's lymphoma: Patients refractory to at least 2 CT lines, and included in tandem auto-allo program 2. Diffuse large B cell lymphoma: Refractory to second line salvage chemotherapy (patients in partial remission, stable disease or progressive). These patients have to be in partial remission, complete remission or stable disease after one o more further CT line. 3. Peripheral T cell lymphoma: Patients failing to achieve a complete remission after first line CT. 4. Low grade lymphomas (follicular and non follicular: Patients refractory to rituximab containing regimens. Patients relapsing after at least 2 lines CT. The duration of remission should be \< 1 year. 5. Chronic lymphatic leukemia: Patients with refractory or relapsing (response duration \< 1 year) disease after R-Fludarabine CT 6. Mantle cell lymphoma: Patients relapsing or refractory after first line conventional CT. * Absence of HLA identical sibling and 10/10 unrelated donor * Patients with adequate physical function as measured by: Cardiac: Left ventricular ejection fraction at rest must be ≥ 40% Hepatic: Bilirubin ≤ 2.5 mg/dL; and ALT, AST, and Alkaline Phosphatase ≤ 5 x ULN. Renal: Creatinine clearance or GFR ≥ 50 mL/min/1.73 m2. Pulmonary: FEV1, FVC, DLCO ≥ 50% predicted (corrected for hemoglobin); if unable to perform pulmonary function tests, then O2 saturation ≥ 92% on room air. Exclusion Criteria: * Presence of HLA-matched, related donor (HLA-A, -B, -DRB1) * Presence of matched unrelated donor (10/10), available on time. * Pregnancy or breast-feeding. * Evidence of HIV infection or known HIV positive serology. * Current uncontrolled bacterial, viral or fungal infection * Evidence of progression of clinical symptoms or radiologic findings. * Prior allogeneic hematopoietic stem cell transplant. * Central Nervous System (CNS) lymphoma localization