Everolimus and Bortezomib in Treating Patients With Relapsed or Refractory Lymphoma

Inclusion Criteria: * Able to provide voluntary written informed consent, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care. * Diagnosed with relapsed or refractory NHL, limited to subtypes listed below. The subject must have histologic information of diagnosis according to review at the Cleveland Clinic Foundation, either at initial diagnosis or at any subsequent relapse. (Biopsy is not required at relapse, but is suggested. Biopsy at outside institution, reviewed at the Cleveland Clinic, is acceptable.) * "Relapsed or refractory" refers to patients who have received at least 1 prior treatment regimen for lymphoma (which may include prior autologous stem cell transplantation) and have demonstrated evidence of progressive disease by clinical and/or radiographic characteristics. * "Indolent lymphoma" is included, and refers to small lymphocytic lymphoma/B-cell chronic lymphocytic leukemia (SLL/CLL); lymphoplasmacytic lymphoma (with or without Waldenstrom's macroglobulinemia); hairy cell leukemia; follicular lymphoma (FL) of any grade; marginal zone B-cell lymphoma; or mantle cell lymphoma. * Transformed lymphoma is included if patients are ineligible for (or refuse) hematopoetic stem cell transplant. * In addition, cutaneous B and T cell lymphoma are permitted. Cutaneous T cell lymphoma must be refractory to 1 prior systemic therapy (topical therapy, photopheresis, radiation are not considered systemic therapy). Transformed B and T cell cutaneous lymphoma are also permitted. * Relapsed/refractory diffuse large B cell lymphoma (DLBCL) is allowed if the patient is not eligible for, or refuses, hematopoetic stem cell transplant. * Relapsed/refractory nodal, leukemic, and extranodal T cell lymphomas are eligible. Subtypes eligible include anaplastic large cell lymphoma, angioimmunoblastic T cell lymphoma, PTCL-NOS, nasal or disseminated extranodal T/NK lymphoma, enteropathy-associated T cell lymphoma, hepatosplenic gamma/delta T cell lymphoma, subcutaneous panniculitis-like T cell lymphoma, T-prolymphocytic leukemia, Adult T-cell leukemia/lymphoma, large granular lymphocytic leukemia, aggressive NK leukemia. * Plasma cell myeloma and Hodgkin lymphoma are excluded. * Prior therapy with bortezomib is allowed. Patients who have received prior bortezomib therapy must have received bortezomib \>6 months ago, and must have shown some response. Patients that did not respond to prior bortezomib therapy are not eligible. * Measurable disease by one of the following: radiographic criteria (≥2 cm by computed tomography); lymphoma involving peripheral blood with more than 5000 leukemia cells/mm3, or any degree of bone marrow infiltration on bone marrow biopsy. Skin involvement with or without nodal or bone marrow involvement permitted for cutaneous lymphomas is also permitted. (see section 6.0, Measurement of Effect). * Eastern Cooperative Group (ECOG) Performance Status of 0-2. * Serum bilirubin levels ≤1.5 times the upper limit of the normal (ULN) range for the laboratory. Higher levels are acceptable if these can be attributed to active hemolysis or ineffective erythropoiesis. Serum AST or serum ALT levels must be ≤2.5 x ULN, or ≤5 x ULN for patients with liver involvement by lymphoma. * Must have adequate bone marrow function: * Absolute neutrophil count (ANC) ≥1,000/uL * Platelet count (Plt) ≥ 75,000/uL * Hemoglobin (Hgb) ≥ 9.0 g/dL * Must have adequate renal function: Creatinine ≤ 1.5 X ULN. * Women of childbearing potential (WCBP) must have a negative serum or urine pregnancy test within 7 days of starting study drug. In addition, sexually active WCBP must agree to use adequate contraceptive methods (tubal ligation; intrauterine device; or barrier contraceptive with spermicide) while on study. Oral, implantable, or injectable contraceptives may be affected by cytochrome P450 interactions, and are therefore not considered effective for this study. WCBP must agree to have pregnancy tests every 4 weeks while on study drug. Male subject agrees to use an acceptable method of contraception for the duration of the study. * Female patients who: * Are postmenopausal for at least 1 year before the Screening visit, OR * Are surgically sterile, OR * If they are of childbearing potential, agree to practice 2 effective methods of contraception, at the same time, from the time of signing the informed consent through 30 days after the last dose of study treatment, OR agree to completely abstain from heterosexual intercourse * Male patients, even if surgically sterilized (ie, status post-vasectomy), who: * Agree to practice effective barrier contraception during the entire study treatment period and through 30 days after the last dose of study treatment, OR * Agree to completely abstain from heterosexual intercourse * Able to adhere to the study visit schedule and other protocol requirements. Exclusion Criteria: * Prior treatment with any investigational drug, chemotherapy, or monoclonal antibody within the preceding 1 month * Chronic treatment with systemic steroids or another immunosuppressive agent. * Patients should not receive immunization with attenuated live vaccines during study period. * History of allogeneic stem cell transplantation. * Any patient with known diabetes mellitus currently requiring insulin therapy, or any patient with preexisting diabetes mellitus in poor control, defined as a hemoglobin A1C (HbA1C) value of over 9% within 4 weeks of starting therapy * Fasting serum cholesterol \>300 mg/dL OR \>7.75 mmol/L or fasting triglycerides \> 2.5 x ULN. NOTE: In case one or both of these thresholds are exceeded, the patient can only be included after initiation of appropriate lipid lowering medication. * Uncontrolled brain or leptomeningeal metastases, including patients who continue to require glucocorticoids for brain or leptomeningeal metastases. * Other malignancies within the past 3 years except for adequately treated carcinoma of the cervix or basal or squamous cell carcinomas of the skin, or low-risk prostate cancer after curative therapy. * Patients who have any severe and/or uncontrolled medical conditions or other conditions that could affect their participation in the study such as: * unstable angina pectoris, any history of congestive heart failure, any history of known myocardial infarction, uncontrolled cardiac arrhythmia * severely impaired lung function * uncontrolled diabetes as defined by fasting serum glucose \>1.5x ULN, off medications * any active (acute or chronic) or uncontrolled infection/ disorders. * nonmalignant medical illnesses that are uncontrolled or whose control may be jeopardized by the treatment with the study therapy * liver disease including a known history of viral hepatitis B or C, evidence of cirrhosis, chronic active hepatitis or chronic persistent hepatitis * a known history of HIV seropositivity * 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) * Patients with an active, bleeding diathesis * Breast feeding or pregnant females * Patients with a known hypersensitivity to everolimus or other rapamycins (sirolimus, temsirolimus) or to its excipients, or to bortezomib, boron, or mannitol * History of noncompliance to medical regimens * Patients unwilling or unable for any reason (personal, medical, or psychiatric) to comply with the protocol * Patients with preexisting peripheral neuropathy grade ≥ 2 will not be eligible * Patients taking concomitant medications (chronically or within 1 week of study drug administration) which are strong inhibitors of hepatic metabolism via P450/CY3PA4 isoenzyme will be excluded. * Patients who have received hematopoietic growth factors (filgrastim, pegfilgrastim, or sargramostim) within 28 days of first dose of screening. * Patient had myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. Prior to study entry, any ECG abnormality at screening must be documented by the investigator as not medically relevant.