Lenalidomide Combined With Modified DA-EPOCH and Rituximab (EPOCH-R2) in Primary Effusion Lymphoma or KSHV-associated Large Cell Lymphoma

* INCLUSION CRITERIA:
* Any Kaposi sarcoma herpesvirus (KSHV)-positive aggressive B cell lymphomas, such as primary effusion lymphoma (PEL), and KSHV-associated large cell lymphoma that is pathologically confirmed by the National Cancer Institute (NCI) Laboratory of Pathology
* Measurable or assessable lymphoma.
* Any human immunodeficiency virus (HIV) status
* Age 18 years or greater. Because no dosing or adverse event data are currently available on the use of lenalidomide in combination with etoposide, prednisone, vincristine, cyclophosphamide, doxorubicin, and rituximab (EPOCH-R) in participants \<18 years of age, children are excluded from this study but may be eligible for future pediatric trials.
* Eastern Cooperative Oncology Group (ECOG) performance status 0-4.
* Females of childbearing potential (FCBP) must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL within 14 days prior to and again within 1 day before starting lenalidomide and must either commit to continued abstinence from heterosexual intercourse or begin TWO acceptable methods of birth control, one highly effective method and one additional effective method AT THE SAME TIME, at least 28 days before she starts taking lenalidomide. Females of reproductive potential must adhere to the scheduled pregnancy testing as required in the Revlimid Risk Evaluation and Mitigation Strategy (REMS) program. Men must agree to use a latex condom during sexual contact with a FCBP even if they have had a vasectomy. All subjects must be counseled at a minimum of every 28 days about pregnancy precautions and risks of fetal exposure. Risks of Fetal Exposure, Pregnancy Testing Guidelines and Acceptable Birth Control
* All study participants must agree to be registered into the mandatory REVLIMID REMS program, and be willing and able to comply with the requirements of the REVLIMID REMS program.
* Able to take aspirin 81mg orally daily or if intolerant of aspirin, able to take a substitute thromboprophylaxis such as low molecular weight heparin.
* Ability of subject to understand and the willingness to sign a written informed consent document.

EXCLUSION CRITERIA:

* Use of other systemic anticancer treatments or agents within the past 2 weeks. The use of rituximab for the treatment of KSHV-associated multicentric Castleman disease (MCD) or KSHV inflammatory cytokine syndrome (KICS) or the use of steroids are allowed within 2 weeks prior to start of treatment.
* Phase I or Phase II participants who have received prior dose-adjusted EPOCH for treatment for PEL or KSHV-associated large cell lymphoma
* Phase II participants who have received any prior curative-intent therapy for PEL or KSHV-associated large cell lymphoma. Participants who have received prior treatment as a bridge to curative-intent therapy will be considered per PI discretion.
* Parenchymal brain involvement with lymphoma
* History of malignant tumors other than KS or KSHV-associated MCD, unless:

  * In complete remission for greater than or equal to 1 year from the time response was first documented or
  * Completely resected basal cell carcinoma or
  * In situ squamous cell carcinoma of the cervix or anus
* Inadequate renal function, defined as calculated or estimated creatinine clearance \< 60 mL/min unless lymphoma, KSHV-MCD, or KICS- related for calculation of creatinine clearance)
* Inadequate hepatic function
* Bilirubin (total) \> 1.5 times the upper limit of normal; aspartate aminotransferase (AST) and/or alanine aminotransferase (ALT) \> 3 times the upper limit of normal; EXCEPTIONS:

  * Total bilirubin greater than or equal to 5 mg/dL in participants with Gilbert's syndrome as defined by \>80% unconjugated
  * Total bilirubin greater than or equal to 7.5 with direct fraction \> 0.7 if participants is receiving a protease inhibitor at the time of initial evaluation
  * Hepatic dysfunction attributed to lymphoma, KSHV-MCD, or KICS
* Absolute neutrophil count (ANC) \<1000/mm\^3 and platelets \< 75,000/mm\^3 unless lymphoma, KSHV-MCD, or KICS- related.
* Common Terminology Criteria for Adverse Events (CTCAE)v5.0 Grade 3-4 neuropathy
* Ejection fraction less than 40% by echocardiography
* Known drug-related, inherited, or acquired procoagulant disorder including prothrombin gene mutation 20210, antithrombin III deficiency, protein C deficiency, protein S deficiency and antiphospholipid syndrome but not including heterozygosity for the Factor V Leiden mutation or the presence of a lupus anticoagulant in the absence of other criteria for the antiphospholipid syndrome.
* History of hypersensitivity reactions attributed to thalidomide, lenalidomide, or pomalidomide, including prior development of erythema nodosum if characterized by a desquamating rash while taking thalidomide, lenalidomide, or pomalidomide.
* Breast feeding (if lactating, must agree not to breast feed while taking lenalidomide). Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with lenalidomide, breastfeeding should be discontinued if the mother is treated with lenalidomide.
* Uncontrolled severe intercurrent illness including, but not limited to bacterial, fungal, or life-threatening viral infection; symptomatic congestive heart failure; unstable angina pectoris; cardiac arrhythmia; or psychiatric illness/social situations that would limit compliance with study requirements. Participants with severe intercurrent illnesses attributed to lymphoma, KSHV-MCD, or KICS may be eligible per principal investigators (PI's) or designees' discretion.
* Any condition, including laboratory abnormalities, which in the opinion of the Principal Investigator or Lead Associate Investigator, would prohibit administration of planned chemotherapeutic intervention, places the subject at unacceptable risk if they were to participate in the study or confounds the ability to interpret data from the study
* Pregnant women are excluded from this study because lenalidomide is a Category X agent with the potential for teratogenic or abortifacient effects. These potential risks may also apply to other agents used in this study.