Testing the Combination of Anti-cancer Drugs Mosunetuzumab, Polatuzumab Vedotin, and Lenalidomide for the Treatment of Relapsed/Refractory Diffuse Large B-Cell Lymphoma

Inclusion Criteria:

* Patients must have histologically confirmed DLBCL NOS, high-grade B-cell lymphoma, or transformed indolent lymphoma as per the World Health Organization 2022 criteria
* All patients will have relapsed/refractory DLBCL after 1 or more prior lines of therapy with the exception of patients receiving CAR T in second line that have a D score of 3 at day (D)+ 30 through D+ 90
* Patients who progressed/relapsed after prior polatuzumab vedotin are allowed
* For the expansion cohorts only: cohort A must have Deauville score of ≥ 3 with the first 90 days) after standard of care chimeric antigen receptor (CAR) T-cell therapy; cohort B- other patients with relapsed/refractory after 1 or more prior lines of therapy (e.g. relapse after Day 90 from CAR-T, or relapsed after other therapies and were not considered candidates for CAR-T)
* All patients that have failed 1 line of therapy will be eligible with the exception of a 12 patient cohort (A) that will require prior CAR T therapy
* Measurable disease by CT or PET scan, with one or more sites of disease \>= 1.5 cm in longest dimension
* Age \>= 18 years

  * Because no dosing or adverse event data are currently available on the use of mosunetuzumab in combination with polatuzumab vedotin, and lenalidomide in patients \< 18 years of age, children are excluded from this study
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
* Life expectancy \>= 12 weeks
* Absolute neutrophil count \>= 1,000/mcL
* Platelets \>= 50,000/mcL without transfusion for 2 weeks prior to cycle 1 day 1 (C1D1)
* Hemoglobin \>= 9 g/dL
* Total bilirubin =\< 1.5 × institutional upper limit of normal (ULN) (however, patients with known Gilbert disease who have serum bilirubin level =\< 3 × ULN may be enrolled)
* Aspartate transaminase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/ alanine aminotransferase (ALT) (serum glutamic-pyruvic transaminase \[SGPT\]) =\< 3 × ULN (AST and/or ALT =\< 5 × ULN for patients with liver involvement)
* Alkaline phosphatase =\< 2.5 × ULN (=\< 5 × ULN for patients with documented liver involvement or bone metastases)
* Creatinine clearance \>= 30 mL/min/1.73 m\^2 by Cockcroft-Gault: (140- age) × (weight in kg) × (0.85 if female) 72 × (serum creatinine in mg/dL)
* International normalized ratio (INR) and activated partial thromboplastin time (aPTT) =\< 1.5 × ULN (This applies only to patients who do not receive therapeutic anticoagulation; patients receiving therapeutic anticoagulation, such as low-molecular-weight heparin or warfarin, should be on a stable dose.)
* Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial
* For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated

  * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load
* Patients with treated brain metastases are eligible if follow-up brain imaging 6-8 weeks after central nervous system (CNS)-directed therapy shows no evidence of progression or CNS lymphoma
* Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial
* For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, and agreement to refrain from donating eggs, as defined below:

  * Women must remain abstinent or use contraceptive methods with a failure rate of 1% per year during the treatment period and for 3 months after the final dose of mosunetuzumab, 3 months after the final dose of polatuzumab vedotin, and 1 month after the last dose of lenalidomide
  * For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use a condom, and agreement to refrain from donating sperm, as defined below:
  * With female partners of childbearing potential, men must remain abstinent or use a condom during the treatment period, 5 months after the final dose of polatuzumab vedotin, and 1 month after the last dose of lenalidomide
* Some concurrent cancer therapeutics (e.g., prostate, breast hormonal-based therapy) are allowed
* Ability to understand and the willingness to sign a written informed consent document. Legally authorized representatives may sign and give informed consent on behalf of study participants
* Agree to comply with all local requirements of the lenalidomide risk minimization plan

Exclusion Criteria:

* Plasmablastic lymphoma, primary mediastinal B-cell lymphoma, gray zone lymphoma
* Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1) with the exception of alopecia
* Patients who are receiving any other investigational agents or treatments
* Any condition, including the presence of laboratory abnormalities, which places the subject at unacceptable risk if he/she were to participate in the study or confounds the ability to interpret data from the study
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to mosunetuzumab or other agents used in study
* Patients with uncontrolled intercurrent illness
* Uncontrolled or known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection (defined as ongoing signs/symptoms related to the infection without improvement despite appropriate antibiotics, antiviral therapy and/or other treatment) at study enrollment, or any major episode of infection requiring treatment with IV antibiotics or hospitalization (relating to the completion of the course of antibiotics) within 4 weeks prior to first study treatment administration
* Active CNS involvement or detectable disease by lymphoma, including leptomeningeal involvement
* Pregnant women are excluded from this study because mosunetuzumab is bispecific antibody with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with mosunetuzumab, breastfeeding should be discontinued if the mother is treated with mosunetuzumab. These potential risks may also apply to other agents used in this study. Pregnant or breastfeeding, or intending to become pregnant during the study or within 3 months after the final dose of mosunetuzumab, 3 months after the final dose of polatuzumab vedotin, and 1 month after the final dose of lenalidomide
* Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2 or better
* Known or suspected chronic active Epstein-Barr virus (EBV) infection
* Patients with any other significant condition(s) that would make this protocol unreasonably hazardous

  * Current \> grade 1 peripheral neuropathy
  * Prior solid organ transplantation
  * Patients with known or suspected history of hemophagocytic lymphohistiocytosis (HLH)
  * Patients with history of confirmed progressive multifocal leukoencephalopathy (PML)
  * Currently active or uncontrolled autoimmune disease

    * Patients with a history of autoimmune-related hypothyroidism on a stable dose of thyroid replacement hormone may be eligible
    * Patients with controlled type 1 diabetes mellitus who are on an insulin regimen are eligible for the study
    * Patients with a history of disease-related immune thrombocytopenic purpura, autoimmune hemolytic anemia, or other stable autoimmune diseases may be eligible