R-ICE and Lenalidomide in Treating Patients With First-Relapse/Primary Refractory Diffuse Large B-Cell Lymphoma

Inclusion Criteria: * Age \>= 18 years * Phase I: Histological confirmation of expressing CD20 antigen as determined by pathology at the respective institution and central pathology review at Mayo Clinic Rochester; all types of B-cell lymphomas are allowed to participate; patients with primary mediastinal large B-cell (PMLBCL) or transformed lymphoma are allowed to participate * Phase II: Histological confirmation of DLBCL expressing CD20 antigen as determined by pathology at the respective institution and central pathology review at Mayo Clinic Rochester; patients with primary mediastinal large B-cell (PMLBCL) or transformed lymphoma are not allowed to participate * Measurable disease (at least 1 lesion \>= 1.5 cm in diameter) as detected by PET/CT * Only 1 line of previous anti-lymphoma therapy is allowed and not currently receiving any other agent that would be considered as a treatment for the lymphoma; patients must be \>= 2 weeks from prior anti-lymphoma therapy; the use of steroids and/or rituximab up to 1 week prior to registration for management of symptoms is allowed * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-2 * Absolute neutrophil count (ANC) \>= 1500/mm\^3, obtained =\< 7 days prior to registration * Platelet count \>= 75,000/mm\^3, obtained =\< 7 days prior to registration * Total bilirubin =\< 2 x upper limit of normal (ULN) (unless related to lymphoma or Gilbert's disease) OR =\< 5 x ULN for subjects with documented or suspected Gilbert's disease, or related to involvement of the liver by the lymphoma, obtained =\< 7 days prior to registration * Aspartate transaminase (AST) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x ULN unless evidence of the direct liver and/or bone involvement by lymphoma, then =\< 5 x ULN, obtained =\< 7 days prior to registration * PHASE I: Subjects must have calculated creatinine clearance \>= 60 ml/min by Cockcroft-Gault formula, obtained =\< 7 days prior to registration * PHASE II: Subjects must have calculated creatinine clearance \>= 30 ml/min by Cockcroft-Gault formula, obtained =\< 7 days prior to registration * For women of childbearing potential only: Negative pregnancy test =\< 10-14 days prior to registration; NOTE: the patient must have an additional negative pregnancy test =\< 24 hours prior to receiving the initial prescription of lenalidomide, per requirements of the REVLIMID Risk Evaluation and Mitigation Strategies (REMS) program * Provide informed written consent * Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study \[i.e. active treatment and observation\]) * Willing to provide blood samples for correlative research purposes * Considered transplant-eligible, as determined by the opinion of the investigator at the participating institution; the participating institution does not need to be a transplant center but patients can be referred to a transplant center if needed * Willing and able to register into and comply with the mandatory requirements of Celgene's REVLIMID REMS program * Females of reproductive potential are willing and able to adhere to the scheduled pregnancy testing as required by Celgene's REVLIMID REMS program * Willing and able to take aspirin (81 mg) daily as prophylactic anticoagulation (patients intolerant to acetylsalicylic acid \[ASA\] may use warfarin or low molecular weight heparin) Exclusion Criteria: * Any of the following because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * NOTE: patients unwilling or unable to do any of the following are also excluded: * Men must agree to use a latex condom during sexual contact with a female of child-bearing potential even if they have had a successful vasectomy * Women of child bearing potential must agree to use 2 methods of reliable contraception simultaneously * All patients must be counseled at a minimum of every 28 days about pregnancy precautions and risks of fetal exposure * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Immunocompromised patients and patients known to be human immunodeficiency virus (HIV) positive and currently receiving antiretroviral therapy; NOTE: patients known to be HIV positive, but without clinical evidence of an immunocompromised state, are eligible for this trial; patients with HIV on antiretroviral therapy other than zidovudine (AZT) and/or stavudine and without prior acquired immunodeficiency syndrome (AIDS) defining conditions and adequate CD4 count (\> 400) are eligible * History of myocardial infarction =\< 180 days prior to registration or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm; patients must be \>= 2 weeks from prior anti-lymphoma therapy; the use of steroids and/or rituximab up to 1 week prior to registration for management of symptoms is allowed * Other active malignancy =\< 3 years prior to registration; EXCEPTIONS: non-melanotic skin cancer, carcinoma-in-situ of the cervix, or any cancer that, in the judgment of the investigator, has been treated with curative intent and will not interfere with the study treatment plan and response assessment; NOTE: if there is a history of prior malignancy, they must not be receiving other specific treatment such as radiation, chemotherapy, or immunotherapy for their cancer * Unable or unwilling to take any prophylaxis; patients with history of or new/active deep vein thrombosis/embolism/thrombophilia are allowed to participate if they are on appropriate therapeutic anticoagulation during the treatment on the trial; these patients would not need the aspirin with the lenalidomide unless clinically indicated; therefore, patients must be able and willing to receive anticoagulation (prophylaxis versus therapeutic as clinically indicated) * History of radiation therapy to \>= 25% of the bone marrow for other diseases * Receiving erythroid stimulating agents (epoetin alfa \[EPO\]: Procrit, Aranesp) * Patients with active or prior central nervous system (CNS) lymphoma or cerebrospinal fluid involvement with malignant lymphoma cells; NOTE: these patients are usually treated with CNS directed therapy; screening for cerebrospinal fluid (CSF)/CNS involvement is NOT required but can be performed per treating medical doctor (MD) discretion * Active hepatitis B as defined by seropositivity for hepatitis B surface antigen (HBsAg); subjects with positive hepatitis B core antibody titers and normal liver transaminases are allowed provided that antiviral prophylaxis is administered per institutional guidelines; NOTE: subjects with hepatitis C antibody will be eligible provided that they do not have elevated liver transaminases or other evidence of active hepatitis