Pralatrexate With Bendamustine and Total-Body Irradiation Followed by Donor Stem Cell Transplant for the Treatment of Relapsed or Refractory T-Cell Non-Hodgkin Lymphoma

Inclusion Criteria: * Age ≥ 18 years with an HCT-Comorbidity Index (CI) ≤ 5 for patients over 60 years * T-cell non-Hodgkin lymphoma (T-NHL) (2022 World Health Organization \[WHO\] criteria) including primary cutaneous T-NHL that is in untreated or unsuccessfully treated first or subsequent relapse. Patients in morphologic remission (i.e. \< 5% blasts in the bone marrow, if involved) but evidence of minimal residual disease (MRD) by positron emission tomography-computed tomography (PET-CT), multiparameter flow cytometry, cytogenetics/fluorescence in situ hybridization (FISH), or molecular means will be eligible for trial participation * The use of bridging chemotherapy prior to initiation of study treatment is allowed. Patients with symptoms/signs of hyperleukocytosis, white blood cells (WBC) \> 100,000/µL, or with concern for other complications of high tumor burden of high tumor dynamics (e.g. disseminated intravascular coagulation) can be treated with leukapheresis or may receive a cycle of salvage chemotherapy prior to start of study treatment * Karnofsky score ≥ 70; Eastern Cooperative Oncology Group (ECOG) 0-1 * Adequate cardiac function defined as absence of decompensated congestive heart failure and/or uncontrolled arrhythmia and left ventricular ejection fraction ≥ 45% * Bilirubin ≤ 2.5 x institutional upper limit of normal unless elevation is thought to be due to hepatic infiltration by lymphoma, Gilbert's syndrome, or hemolysis * Adequate pulmonary function defined as absence of oxygen (O2) requirements and either diffusion capacity of the lung for carbon monoxide (DLCO) corrected ≥ 70%mmHg or DLCO corrected 60-69%mmHg and partial pressure of oxygen (pO2) ≥ 70mmHg * Creatinine clearance ≥ 60 mL/min * Prior autologous HCT is permissible if relapse occurred \> 6 months after HCT * A human leukocyte antigen (HLA)-matched sibling/unrelated donor mismatched unrelated donor or haploidentical donor for collection of stimulated peripheral blood stem cells must be identified and readily available * If the patient has received pralatrexate or bendamustine before and has been sensitive to this regimen, defined as MRD negative complete response (CR) immediately after receiving the treatment and which lasts ≥ 1 year, eligibility will be determined on a case-by-case basis by the study principal investigator (PI) * Ability to understand and sign a written informed consent document (or legal representative) * RELATED DONOR: Related to the patient and genotypically or phenotypically identical for HLA-A, B, C, DRB1 and DQB1. Phenotypic identity must be confirmed by high-resolution typing * MATCHED UNRELATED DONOR: Matched for HLA-A, B, C, DRB1 and DQB1 by high resolution typing; OR * MATCHED UNRELATED DONOR: Mismatched for a single allele without antigen mismatching at HLA-A, B, or C as defined by high resolution typing but otherwise matched for HLA-A, B, C, DRB1 and DQB1 by high resolution typing * MATCHED UNRELATED DONOR: Donors are excluded when preexisting immunoreactivity is identified that would jeopardize donor hematopoietic cell engraftment. The recommended procedure for patients with 10 of 10 HLA allele level (phenotypic) match is to obtain panel reactive antibody (PRA) screens to class I and class II antigens for all patients before HCT. If the PRA shows \> 10% activity, then flow cytometric or B and T cell cytotoxic cross matches should be obtained. The donor should be excluded if any of the cytotoxic cross match assays are positive. For those patients with an HLA Class I allele mismatch, flow cytometric or B and T cell cytotoxic cross matches should be obtained regardless of the PRA results. A positive anti-donor cytotoxic crossmatch is an absolute donor exclusion. * MATCHED UNRELATED DONOR: Patient and donor pairs homozygous at a mismatched allele in the graft rejection vector are considered a two-allele mismatch, i.e., the patient is A\*0101 and the donor is A\*0102, and this type of mismatch is not allowed. * MISMATCHED UNRELATED DONOR: HLA-matching must be based on results of high resolution typing at HLA-A, -B, -C, -DRB1, and -DQ * MISMATCHED UNRELATED DONOR: Mismatch for one HLA class I antigen with or without an additional mismatch for one HLA-class I allele but matched for HLA-DRB1 and HLA-DQ * MISMATCHED UNRELATED DONOR: Mismatched for two HLA class I alleles but matched for HLA-DRB1 and HLA-DQ * MISMATCHED UNRELATED DONOR: HLA class I HLA-A, -B, -C allele matched donors allowing for any one or two DRB1 and/or DQB1 antigen/allele mismatch * MISMATCHED UNRELATED DONOR: If the patient is homozygous at the mismatch HLA class I locus or II locus, the donor must be heterozygous at that locus and one allele must match the patient (i.e., patient is homozygous A\*01:01 and donor is heterozygous A\*01:01, A\*02:01). This mismatch will be considered a one-antigen mismatch for rejection only * HAPLOIDENTICAL DONOR: Donors must be haploidentical relatives of the patients. Donor-recipient compatibility will be tested through HLA typing at high resolution for the HLA loci (-A, -B, -C, -DRB1, -DQB1). Donor and recipient should share at least 5/10 HLA loci * HAPLOIDENTICAL DONOR: Age ≥ 18 years * HAPLOIDENTICAL DONOR: Weight ≥ 40 kg * HAPLOIDENTICAL DONOR: Donor must meet the selection criteria as defined by the Foundation of the Accreditation of Cell Therapy (FACT) and will be screened per the American Association of Blood Banks (AABB) guidelines * HAPLOIDENTICAL DONOR: In case of more available haploidentical donors, selection criteria should include, in this order: * For cytomegalovirus (CMV) seronegative recipients, a CMV seronegative donor * Red blood cell compatibility * Red blood cell (RBC) cross match compatible * Minor ABO incompatibility * Major ABO incompatibility Exclusion Criteria: * Active central nervous system (CNS) disease * Concomitant illness associated with a likely survival of \< 1 year * Active systemic fungal, bacterial, viral, or other infection, unless disease is under treatment with antimicrobials and/or controlled or stable. Patients with fever thought to be likely secondary to myeloid malignancy are eligible * Known hypersensitivity or contraindication to any study drug used in this trial * Pregnancy or lactation * Concurrent treatment with any other approved or investigational anti-lymphoma agent at the time of starting conditioning * HAPLOIDENTICAL DONOR: Since detection of anti-donor-specific antibodies (anti-DSA) is associated with higher graft rejection rate, patients will be screened for anti-DSA pre-transplant. Patient with DSA mean fluorescent intensity (MFI) \< 5000 after desensitization treatment, will be considered eligible to participate in the study