Combination Chemotherapy and Pralatrexate as First-Line Therapy in Treating Patients With Non-Hodgkin Lymphoma

Inclusion Criteria: * Histologically confirmed new diagnosis of Stage II, III and IV peripheral T-cell NHL not otherwise specified (NOS), anaplastic large cell lymphoma (ALK negative) (ALK positive if international prognostic index \[IPI\] 3, 4, or 5), angioimmunoblastic T-cell lymphoma, enteropathy associated T-cell lymphoma, hepatosplenic gamma delta T-cell lymphoma * Pathology material (hematoxylin and eosin \[H\&E\] stain, immunohistochemistry \[IHC\] and pathology report from initial diagnosis, if slides are not available, then 8 unstained slides of 4 micron thickness or a representative block should be sent) will be reviewed, and the diagnosis confirmed by University Nebraska Medical Center (UNMC) pathology department (retrospective diagnostic review: treatment may commence prior to the UNMC review) * No prior therapy with the exception of prior radiation therapy and 1 cycle of chemotherapy based on current diagnosis and clinical condition * Age 19 years or older (the age of consent in Nebraska); age 18 years or older (applicable to states where the age of majority is 18) * Expected survival duration of \>= six months * Karnofsky Performance Status \>= 70 * Absolute neutrophil count (ANC) \>= 1000 cells/mm\^3, unless due to lymphoma involvement of the bone marrow * Platelet Count \>= 100 mm\^3, unless due to lymphoma involvement of the bone marrow * Total bilirubin =\< 1.5 x upper normal limit (ULN), or =\< 3 x ULN if documented hepatic involvement with lymphoma, or =\< 5 x ULN if history of Gilbert's Disease * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x ULN (=\< 5 x ULN if documented hepatic involvement with lymphoma) * Serum potassium within normal range * Serum creatinine \< 2.0 mg/dL or calculated creatinine clearance (CrCl) \> 45 mL/min * Prothrombin time (PT) or international normalized ratio (INR), and partial thromboplastin time (PTT) =\< 1.5 x ULN unless patient is receiving anticoagulants; if patient is on anticoagulation therapy, levels should be within therapeutic range * Patients with measurable disease; patients with non-measurable but evaluable disease may be eligible after discussion with the principal investigator (PI); baseline measurements and evaluations must be obtained within 6 weeks of registration to the study; abnormal positron emission tomography (PET) scans will not constitute evaluable disease, unless verified by computed tomography (CT) scan or other appropriate imaging * Patients with measurable disease must have at least one objective measurable disease parameter; a clearly defined, bidimensionally measurable defect or mass measuring at least 2 cm in diameter on a CT scan will constitute measurable disease; proof of lymphoma in the liver is required by a confirmation biopsy * Women must not be pregnant or breast-feeding due to teratogenic effects of chemotherapy * All females of childbearing potential must have a blood test within 2 weeks prior to registration to rule out pregnancy * Pregnancy testing is not required for post-menopausal or surgically sterilized women * Male and female patients of reproductive potential must agree follow accepted birth control measures * Patient must be able to adhere to the study visit schedule and other protocol requirements * Patients must be willing to give written informed consent, and sign an institutionally approved consent form before performance of any study-related procedure not part of normal medical care; with the exception of 1 cycle of chemotherapy based on current diagnosis and clinical condition, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care * No serious disease or condition that, in the opinion of the investigator, would compromise the patient's ability to participate in the study Exclusion Criteria: * Pregnant or breast feeding females * Known positive for human immunodeficiency virus (HIV), human T-lymphotropic virus type 1 (HTLV-1), or infectious hepatitis, type A, B or C or active hepatitis * Major surgery within 2 weeks of study drug administration * Prior malignancies within the past 3 years with exception of adequately treated basal cell, squamous cell skin cancer, or thyroid cancer; carcinoma in situ of the cervix or breast; prostate cancer of Gleason Grade 6 or less with stable prostate-specific antigen (PSA) levels * Patients with a diagnosis of other peripheral T-cell lymphoma (PTCL) histologies other than those specified in the inclusion criteria * Contraindication to any of the required concomitant drugs or supportive treatments, including hypersensitivity to all anticoagulation and antiplatelet options, antiviral drugs, or intolerance to hydration due to preexisting pulmonary or cardiac impairment * Any other clinically significant medical disease or condition laboratory abnormality or psychiatric illness that, in the Investigator's opinion, may interfere with protocol adherence or a subject's ability to give informed consent * Concomitant administration of nonsteroidal anti-inflammatory drugs (NSAIDs) and trimethoprim/sulfamethoxazole will not be allowed, since these may result in delayed clearance of pralatrexate