Tafasitamab and Lenalidomide Followed by Tafasitamab and ICE as Salvage Therapy for Transplant Eligible Patients With Relapsed/ Refractory Large B-Cell Lymphoma

Inclusion Criteria: * Adult patient (age 18 or older) * Willing and able to provide written informed consent for the trial, assent when appropriate may be obtained per institutional guidelines * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Considered transplant eligible by the treating physician * Measurable disease by CT (defined as \>= 1.5 cm in diameter) or one or more area of PET avid disease * Have received one line of prior chemo-immunotherapy (i.e. cyclophosphamide, doxorubicin, prednisone, rituximab and vincristine \[R-CHOP\]). Note that corticosteroids for palliation of symptoms and radiation consolidation are not considered a line of therapy for purposes of eligibility determination * Eligible histologic diagnosis includes: Diffuse large B cell lymphoma not otherwise specified (NOS), T cell histiocyte rich large B cell lymphoma, primary mediastinal B Cell lymphoma, follicular lymphoma grade 3B, high grade B cell lymphoma with MYC and BCL2 and/or BCL6 rearrangement, high grade B cell lymphoma NOS, DLBCL transformed from follicular lymphoma, DLBCL transformed from marginal zone lymphoma, DLBCL leg type, and B cell lymphoma unclassifiable (with features intermediate between DLBCL and classical Hodgkin's lymphoma) * Absolute neutrophil count \>= 1000 / mcL * Platelets \>= 75,000 / mcL in absence of transfusion support within 7 days of determining eligibility * Hemoglobin \>= 8.0 g/dL, with exception of cases in which cytopenias are due to marrow involvement by lymphoma * Serum total bilirubin =\< 1.5 x upper limit of normal (ULN) (except in patients with Gilbert Syndrome who can have total bilirubin \< 3.0 mg/dL) * Aspartate transaminase (AST) and alanine transaminase (ALT) =\< 3.0 x ULN * Serum creatinine clearance \>= 60 mL/min (calculated according to institutional standard) * Female subjects of childbearing potential should have a negative serum pregnancy test at screening and within 24 hours of receiving the first dose of study medication * Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 3 months following the last dose of study treatment. Subjects should agree to ongoing pregnancy testing during the course of the study and after the end of study therapy. Subjects of childbearing potential are patients who have not been surgically sterilized and have not been free from menses for \> 1 year * Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 3 months after the last dose of study therapy. Males must refrain from donating sperm during study participation and for 3 months after last dose of study medication * In the opinion of the investigator, patients must be able and willing to receive adequate prophylaxis and/or therapy for thromboembolic events and be able to understand the reason for complying with the special conditions of the pregnancy prevention risk management plan * Willing to provide archival tissue from biopsy performed after frontline systemic therapy (If prior archival tissue is unavailable, exceptions may be granted by the study principal investigator \[PI\]) Exclusion Criteria: * Known active central nervous system involvement by lymphoma, including leptomeningeal involvement * DLBCL transformed from chronic lymphocytic leukemia or small lymphocytic lymphoma (Richter's syndrome) * Prior solid organ transplant * Prior hematopoietic cell transplant * History of other malignancy that could affect compliance with the protocol or interpretation of results in the opinion of the investigator * Myocardial infarction or cerebrovascular accident within the past 6 months * Clinically significant cardiovascular disease including uncontrolled arrhythmia or New York Heart Association Class 2-4 congestive heart failure * Active uncontrolled infection or infection requiring IV antibiotic therapy * Major surgery within 4 weeks prior to start of treatment other than surgery performed for diagnosis * Prior lymphoma therapy should be completed greater than two weeks from the start of protocol therapy, with exception of patients receiving corticosteroids for palliation of symptoms * Human immunodeficiency virus (HIV) infection AND CD4 count \< 350 cells/ mm\^3, evidence of resistant strain of HIV, or HIV viral load \>= 50 copies HIV ribonucleic acid (RNA)/mL if on highly active antiretroviral therapy (HAART) or HIV viral load \>= 10,000 copies HIV RNA/mL if not on anti-HIV therapy * Known active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection. Patients with past HBV infection (defined as negative hepatitis B surface antigen \[HBsAg\] and positive hepatitis B core antibody \[HBcAb\]) are eligible if HBV DNA is undetectable. Patients who are positive for HCV antibody are eligible if polymerase chain reaction (PCR) is negative for HCV RNA. Testing to be done only in patients suspected of having infections or exposures * Known contraindication to any medication in the treatment plan, including known hypersensitivity * Prior treatment with anti-CD19 targeted therapy or lenalidomide * Gastrointestinal abnormalities including the inability to take oral medication, requirement of intravenous alimentation, or prior surgical procedure resulting in impaired enteral absorption of medication * History or evidence of rare hereditary problems of galactose intolerance, the Lapp lactase deficiency, or glucose-galactose malabsorption * History of deep venous thromboembolism threatening thromboembolism, or known thrombophilia AND not willing to take venous thromboembolism prophylaxis during the study period * Patients who in the opinion of the investigator have not recovered sufficiently from the adverse toxic events of prior therapy