Intravenous Vesicular Stomatitis Virus in Patients With Peripheral T-cell Lymphoma

Inclusion Criteria: * Age \>= 18 years * Relapsed or refractory: * Group E only: Relapsed peripheral T-cell lymphoma (PTCL) of the following histologies: peripheral T-cell lymphoma-NOS (PTCL-NOS); anaplastic large cell (ALCL), and mycosis fungoides (MF) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2 times upper limit of normal (ULN) (obtained =\< 15 days prior to registration) * Creatinine =\< 2.0 mg/dL (obtained =\< 15 days prior to registration) * Direct bilirubin =\< 1.5 x ULN (obtained =\< 15 days prior to registration) * International normalized ratio (INR)/prothrombin time (PT) and activated partial thromboplastin time (aPTT) =\< 1.5 x ULN (obtained =\< 15 days prior to registration) * If baseline liver disease, Child Pugh score not exceeding class A (obtained =\< 15 days prior to registration) * Negative pregnancy test for persons of child-bearing potential (obtained =\< 15 days prior to registration) * FOR T-Cell Lymphoma (TCL)/B-Cell Lymphoma (BCL) ONLY: Absolute Neutrophil Count (ANC) \>= 1,000/microliter (μL) (obtained =\< 14 days prior to registration) * FOR TCL/BCL ONLY: Platelets \>= 100,000/μL (obtained =\< 14 days prior to registration) * FOR TCL/BCL ONLY: Hemoglobin \>= 8.5 g/dl (obtained =\< 14 days prior to registration) * FOR TCL/BCL ONLY: Measurable disease by CT or magnetic resonance imaging (MRI): must have at least one lesion that has a single diameter of \> 2 cm or tumor cells in the blood \> 5 x 10\^9/L; NOTE: skin lesions can be used if the area is \> 2 cm in at least one diameter and photographed with a ruler and the images are available in the medical record * Absence of active central nervous system (CNS) involvement; NOTE: pre-enrollment lumbar puncture not mandatory * Ability to provide written informed consent * Willingness to return to Mayo Clinic for follow-up * Life expectancy \>= 12 weeks * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2 * Willing to provide mandatory biological specimens for research purposes Exclusion Criteria: * Availability of and patient acceptance of curative therapy * Uncontrolled infection * Active tuberculosis or hepatitis, or chronic hepatitis * Any of the following prior therapies: * Chemotherapy (IMIDs, alkylating agents, proteosome inhibitors) =\< 2 weeks prior to registration * Immunotherapy (monoclonal antibodies) =\< 4 weeks prior to registration * Experimental agent in case of Acute Myeloid Leukemia (AML) or TCL within 4 half-lives of the last dose of the agent * New York Heart Association classification III or IV, known symptomatic coronary artery disease, or symptoms of coronary artery disease on systems review, or known cardiac arrhythmias \[atrial fibrillation or supraventricular tachycardia (SVT)\] * Active CNS disorder or seizure disorder or known CNS disease or neurologic symptomatology; in case of AML active CNS involvement as detected by lumbar puncture or neuro-imaging (only to be done if clinically indicated) * Human immunodeficiency virus (HIV) positive test result or other immunodeficiency or immunosuppression * Other concurrent chemotherapy, immunotherapy, radiotherapy, or any ancillary therapy considered investigational (used for a non-Food and Drug Administration \[FDA\] approved indication and in the context of a research investigation); * NOTE: in TCL, patients may use topical emollients or corticosteroids, acetic acid soaks, etc. to control pruritis and prevent infection; no topical chemotherapy is allowed (no topical nitrogen mustard) * Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown: * Pregnant women or women of reproductive ability who are unwilling to use effective contraception * Nursing women * Men who are unwilling to use a condom (even if they have undergone a prior vasectomy) while having intercourse with any woman, while taking the drug and for 4 weeks after stopping treatment * ADDITIONAL EXCLUSION CRITERIA FOR GROUP E (COMBINATION WITH IPILIMUMAB AND CEMIPLIMAB) ONLY: * Diagnosis of AML * Diagnosis of Angioimmunoblastic T-cell Lymphoma (AITL) * Hypersensitivity to ipilimumab or its excipients