Everolimus and Lenalidomide in Treating Patients With Relapsed or Refractory Non-Hodgkin or Hodgkin Lymphoma

Inclusion * Histological or cytological confirmation of relapsed or refractory non-Hodgkin lymphoma or Hodgkin lymphoma =\< 6 months prior to registration * The following disease types are eligible: Study 1 - Aggressive lymphomas- Transformed lymphomas; Diffuse large B cell lymphoma; Mantle cell lymphoma; Follicular lymphoma grade III; Precursor B lymphoblastic leukemia/lymphoma; Mediastinal (thymic) large B-cell lymphoma; Burkitt lymphoma/leukemia; Precursor T lymphoblastic leukemia/lymphoma; Primary cutaneous anaplastic large cell lymphoma; and Anaplastic large cell lymphoma-primary systemic type * Study 2- Indolent lymphomas: Follicular lymphoma, grades 1, 2; Extranodal marginal zone B-cell lymphoma of MALT type; Nodal marginal zone B-cell lymphoma; Splenic marginal zone B-cell lymphoma; Small lymphocytic lymphoma * Study 3- Uncommon lymphomas: Peripheral T cell lymphoma, unspecified; Anaplastic large cell lymphoma (T and null cell type); Lymphoplasmacytic lymphoma (Waldenstrom Macroglobulinemia); Post transplant lymphoproliferative disorders; Mycosis fungoides/Sezary syndrome; Hodgkin Disease; Primary effusion lymphoma; Adult T-cell leukemia/lymphoma; Extranodal NK/T-cell lymphoma, nasal type; Enteropathy-type T-cell lymphoma; Hepatosplenic T-cell lymphoma; Subcutaneous panniculitis-like T-cell lymphoma; Angioimmunoblastic T-cell lymphoma; Anaplastic large cell lymphoma-primary cutaneous type; and Blastic plasmacytoid dendritic cell neoplasm * Measurable disease by CT or MRI or PET/CT: Must have at least one lesion that has a single diameter of \>= 2 cm or tumor cells in the blood \>= 5 x10\^9/L (Skin lesions can be used if the area is \>= 2 cm in at least one diameter and photographed with a ruler) * For lymphoplasmacytic lymphoma patients without measurable lymphadenopathy, measurable disease is defined by both of the following criteria: Bone marrow lymphoplasmacytosis with \> 10% lymphoplasmacytic cells or aggregates, sheets, lymphocytes, plasma cells, or lymphoplasmacytic cells on bone marrow biopsy and quantitative IgM monoclonal protein \> 800 mg/dL * ANC \>= 1200/uL * Hgb \> 9 g/dl * PLT \>= 50,000/uL * Total bilirubin =\< 1.5 x upper limit of normal (ULN) or if total bilirubin is \> 1.5 x ULN the direct bilirubin must be normal * AST =\< 2.5 x ULN or AST =\< 5 x ULN if liver involvement * Creatinine =\< 1.5 x ULN * Creatinine clearance \>= 50mL/min (Cockcroft-Gault calculation) * Fasting serum cholesterol =\< 300 mg/dL OR =\< 7.75 mmol/L AND fasting triglycerides =\< 2.5 x ULN (NOTE: Lipid lowering medication is allowed) * ECOG Performance Status (PS) 0, 1, or 2 * Females of childbearing potential (FCBP) must have a negative serum pregnancy test with a sensitivity of at least 50 IU/ml within 10-14 days prior to and again within 24 hours of 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, during study treatment and for 8 weeks after the last dose of RAD001 (FCBP must also agree to ongoing pregnancy testing) * Men must agree to use a latex condom during sexual contact with a FCBP even if they have had a successful vasectomy (All patients must be counseled at a minimum of every 28 days about pregnancy precautions and risks of fetal exposure) * Provide informed written consent * Willingness to return to Mayo Clinic enrolling institution for follow-up * Patient is willing to provide blood samples for research purposes * Recovered from acute side effects of prior myelosuppressive chemotherapy or biological therapy * All study participants must be registered into the mandatory RevAssist program, and be willing and able to comply with the requirements of RevAssist Exclusion * 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 * Active other malignancy, excepting non-melanotic skin cancer or carcinoma-in-situ of the cervix (If there is a history of prior malignancy, they must not be receiving other specific treatment (other than hormonal therapy) for their cancer) * History of myocardial infarction =\< 6 months, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias * Any of the following because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects; Nursing women; Men or women of childbearing potential who are unwilling to employ adequate contraception throughout the study and for 8 weeks after the last dose of study drug (NOTE: If barrier contraceptives are being used, these must be continued throughout the trial by both sexes; hormonal contraceptives are not acceptable as a sole method of contraception) * Patients who have received prior treatment with both an mTOR inhibitor (sirolimus, temsirolimus, everolimus) and lenalidomide who did not have a response to either when used as single agents * Patients with a known allergic reaction to thalidomide, RAD001 (everolimus) or other rapamycins (sirolimus, temsirolimus) or their excipients to the point where either agent should not be given again * The development of erythema nodosum if characterized by a desquamating rash while taking thalidomide or similar drugs * Known positive for HIV or infectious hepatitis, type A, B or C * Patients, who have had a major surgery or significant traumatic injury within 4 weeks of start of study drug, patients who have not recovered from the side effects of any major surgery (defined as requiring general anesthesia) or patients that may require major surgery during the course of the study * Immunization with attenuated live vaccines within one week of study entry or during study period * Uncontrolled brain or leptomeningeal metastases, including patients who continue to require glucocorticoids for brain or leptomeningeal metastases * Impairment of gastrointestinal function or gastrointestinal disease that may significantly alter the absorption of RAD001 (e.g., ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome or small bowel resection) * Prior Allogeneic Stem Cell Transplant * No chronic treatment with systemic steroids or another immunosuppressive agents (at a dose equivalent of greater than 20 mg prednisone per day) or other immunosuppressive agents)