Gemcitabine Hydrochloride, Clofarabine, and Busulfan Before Donor Stem Cell Transplant in Treating Patients With Refractory B-Cell or T-Cell Non-Hodgkin Lymphoma or Hodgkin Lymphoma

Prior treatment

• Pregnancy (positive beta human chorionic gonadotropin \[HCG\] test in a woman with child bearing potential defined as not post-menopausal for 12 months or no previous surgical sterilization) or currently breast-feeding; pregnancy testing is not required for post-menopausal or surgically sterilized women
• Exposure to other investigational drugs within 2 weeks before enrollment
• Grade \>= 3 non-hematologic toxicity from previous therapy that has not resolved to =\< grade 1
• Radiation therapy to head and neck (excluding eyes), and internal organs of chest, abdomen or pelvis in the month prior to enrollment
• Prior whole brain irradiation
• Prior autologous stem-cell transplant (SCT) in the prior 3 months

Other illness

• Patient with active central nervous system (CNS) disease
• Active hepatitis B, either active carrier (hepatitis B virus surface antigen \[HBsAg\] +) or viremic (hepatitis B virus \[HBV\] deoxyribonucleic acid \[DNA\] \>= 10,000 copies/mL, or \>= 2,000 IU/mL)
• Evidence of either cirrhosis or stage 3-4 liver fibrosis in patients with chronic hepatitis C or positive hepatitis C serology
• Human immunodeficiency virus (HIV) infection
• Active uncontrolled bacterial, viral or fungal infections

• Patients with refractory B-cell or T-cell non-Hodgkin's lymphoma or Hodgkin's lymphoma who are eligible for allogeneic transplantation
• An 8/8 human leukocyte antigen (HLA) matched (high resolution typing at A, B, C, DRB1) sibling or unrelated donor
• Left ventricular ejection fraction (EF) \>= 45%
• Forced expiratory volume in one second (FEV1) \>= 50%
• Forced vital capacity (FVC) \>= 50%
• Diffusing capacity of the lung for carbon monoxide (DLCO) \>= 50%
• Estimated serum creatinine clearance \>= 50 ml/min (using the Cockcroft-Gault formula)
• Serum creatinine =\< 1.6 mg/dL
• Serum bilirubin =\< 2 x upper limit of normal
• Serum glutamate pyruvate transaminase (SGPT) =\< 2 x upper limit of normal
• Voluntary signed Institutional Review Board (IRB)-approved informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care
• Men and women of reproductive potential must agree to follow accepted birth control methods for the duration of the study; female subject is either post-menopausal or surgically sterilized or willing to use an acceptable method of birth control (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study; male subject agrees to use an acceptable method for contraception for the duration of the study