Panobinostat and Everolimus in Treating Patients With Recurrent Multiple Myeloma, Non-Hodgkin Lymphoma, or Hodgkin Lymphoma

Inclusion Criteria: * Relapsed or refractory multiple myeloma requiring therapy, who have failed, unable to tolerate, or refused other available active therapies * Biopsy-proven relapsed or refractory non-Hodgkin lymphoma or Hodgkin disease requiring treatment, who have failed, unable to tolerate, or refused other available active therapies; patients should not have other treatment options considered curative; (NOTE: for patients with lymphoma, a re-biopsy is necessary unless the patient has had a previous biopsy \< 6 months prior to treatment on this protocol if there has been no intervening treatment; patients with biopsy-proven central nervous system \[CNS\] lymphoma at any time are not required to have a re-biopsy to be eligible for this study) * Multiple myeloma: * Serum monoclonal protein \>= 1.0 g/dL * \>= 200 mg of monoclonal protein in the urine on 24 hour electrophoresis * Serum immunoglobulin free light chain \>= 10 mg/dL AND abnormal serum immunoglobulin kappa to lambda free light chain ratio * Monoclonal bone marrow plasmacytosis \>= 30% (evaluable disease) at time of registration * Lymphoma: * Measurable disease by computed tomography (CT) or magnetic resonance imaging (MRI) or the CT portion of the positron emission tomography (PET)/CT; must have at least one lesion that has a single diameter of \>= 2 cm or tumor cells in the blood \>= 5 x 10\^9/L; skin lesions can be used if the area is \>= 2 cm in at least one diameter and photographed with a ruler * The following disease types are eligible: * 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 * Anaplastic large cell lymphoma - primary systemic type * Small lymphocytic lymphoma/chronic lymphocytic leukemia * Follicular lymphoma, grades 1, 2 * Extranodal marginal zone B-cell lymphoma of mucosa-associated lymphoid tissue (MALT) type * Nodal marginal zone B-cell lymphoma * Splenic marginal zone B-cell lymphoma * Peripheral T cell lymphoma, unspecified. * Anaplastic large cell lymphoma (T and null cell type) * Lymphoplasmacytic lymphoma (Waldenstrom Macroglobulinemia) * CNS lymphoma * Post transplant lymphoproliferative disorders * Mycosis fungoides/Sezary syndrome * Hodgkin Disease * Primary effusion lymphoma * Blastic natural killer (NK)-cell 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 * For lymphoplasmacytic lymphoma patients without measurable lymphadenopathy, measurable disease can be 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 immunoglobulin (Ig)M monoclonal protein \> 1,000 mg/dL * Absolute neutrophil count (ANC) \>= 1000/uL * Hemoglobin (Hgb) \>= 9 g/dl * Platelets (PLT) \>= 75,000/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 * Aspartate aminotransferase (AST) =\< 3 x ULN * Creatinine =\< 2.5 x ULN * Serum potassium, magnesium and phosphorus \>= lower limit of normal (LLN) and =\< 1.2 x ULN * Ionized calcium \>= LLN * Thyroid-stimulating hormone (TSH) =\< 1.5 x ULN; patients are permitted to receive thyroid hormone supplements to treat underlying hypothyroidism * Ability to understand and the willingness to sign a written informed consent document * Willingness to return to Mayo Clinic or National Cancer Institute, National Institutes of Health (NIH) - Medical Oncology Branch, Center for Cancer Research (CCR) * Life expectancy \>= 12 weeks * Willing to provide blood samples for research studies as required by the protocol * Negative pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2 Exclusion Criteria: * Candidate for known standard therapy for the patient's disease that is potentially curative * Uncontrolled infection * Therapy with myelosuppressive chemotherapy or biologic therapy \< 3 weeks unless the patient has recovered from the nadir of the previous treatment to a level that meets the inclusion eligibility criteria of this protocol; NOTE: patients who have received prior RAD001 therapy will be allowed but must meet above requirements * Receiving corticosteroids \> 20 mg of prednisone per day (or equivalent); NOTE: patients may be receiving stable (not increased within the last month) chronic doses of corticosteroids with a maximum dose of 20 mg of prednisone per day if they are being given for disorders other than lymphoma (with the exception of CNS lymphoma, which steroids are permitted at the lowest possible dose necessary and should not be escalated during treatment) such as rheumatoid arthritis, polymyalgia rheumatica or adrenal insufficiency, or asthma * Persistent toxicities \>= grade 2 from prior chemotherapy or biological therapy regardless of interval since last treatment * Impaired cardiac function or clinically significant cardiac diseases, including any one of the following: * Patients with congenital long QT syndrome * History or presence of sustained ventricular tachyarrhythmia; (patients with a history of atrial arrhythmia are eligible but should be discussed with the Sponsor prior to enrollment) * Any history of ventricular fibrillation or torsade de pointes * Bradycardia defined as heart rate (HR) \< 50 beats per minute (bpm;) patients with pacemakers are eligible if HR \>= 50 bpm * Screening electrocardiogram (ECG) with a QTcFredericia (QTcF) \> 450 msec * Right bundle branch block + left anterior hemiblock (bifascicular block) * Patients with myocardial infarction or unstable angina =\< 6 months prior to starting study drug * Other clinically significant heart disease (e.g., congestive heart failure \[CHF\] New York \[NY\] Heart Association class III or IV, uncontrolled hypertension, history of labile hypertension, or history of poor compliance with an antihypertensive regimen) * Any of the following: * Pregnant women or women of reproductive ability who are unwilling to use effective contraception * Nursing women * Men who are unwilling to use a condom (even if they have undergone a prior vasectomy) while having intercourse with any woman, while taking the drug and for 4 weeks after stopping treatment * Other concurrent chemotherapy, immunotherapy, radiotherapy, or any ancillary therapy considered investigational (utilized for a non-Food and Drug Administration \[FDA\]-approved indication and in the context of a research investigation); NOTE: patients may undergo palliative concurrent radiation of myeloma lesions for pain control or impending fracture, provided the lesion(s) by themselves do not constitute progression * Known positivity for human immunodeficiency virus (HIV) or hepatitis C with uncontrolled disease; baseline testing for HIV is not required; Note: a detailed assessment of Hepatitis B/C medical history and risk factors must be done at screening for all patients; hepatitis b virus (HBV) deoxyribonucleic acid (DNA) and hepatitis C virus (HCV) ribonucleic acid (RNA) polymerase chain reaction (PCR) testing are required at screening for all patients with a positive medical history based on risk factors and/or confirmation of prior HBV infection * Active other malignancy requiring treatment that would interfere with the assessments of response of the lymphoma or myeloma to protocol treatment * Inability to swallow or impairment of gastrointestinal function or gastrointestinal disease that may significantly alter the absorption of the drugs (e.g., ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome or small bowel resection) that would preclude use of oral medications * Thrombotic or embolic events such as a cerebrovascular accident including transient ischemic attacks within the past 6 months * Any severe and/or uncontrolled medical conditions or other conditions that, in the treating physician's opinion, could adversely impact their ability to participate in the study; NOTE: patients on chronic oxygen therapy, those with liver disease such as cirrhosis, chronic hepatitis or chronic persistent hepatitis, or uncontrolled infections will be excluded * Known hypersensitivity to RAD001 (everolimus) or other rapamycins (sirolimus, temsirolimus) * Receiving any medications or substances that are strong or moderate inhibitors of CYP3A4; receiving any medications or substances that are inducers of CYP3A4 * Using medications that have a relative risk of prolonging the QT interval or inducing torsade de pointes if treatment cannot be discontinued or switched to a different medication prior to starting study drug * Active bleeding tendency; NOTE: patients on therapeutic anticoagulation should be monitored carefully to maintain therapeutic level of anticoagulation to avoid increased risk of bleeding due to concurrent drug induced thrombocytopenia; it is suggested that patients who require anticoagulation therapy while on therapy use low molecular weight heparin (LMWH) * Major surgery =\< 4 weeks prior to registration or have not recovered from side effects of such therapy