Everolimus and Alemtuzumab in Treating Patients With Recurrent Chronic Lymphocytic Leukemia or Small Lymphocytic Lymphoma

Inclusion

* Diagnosis of CLL manifested by minimum threshold peripheral lymphocyte count of \> 5 x 10\^9/L (CLL variant) OR palpable adenopathy \>= 1cm or clinically palpable splenomegaly (SLL variant); AND immunophenotypic demonstrations of a population of B lymphocytes (as defined by CD19+) which are monoclonal (by light chain exclusion)
* CLL will be diagnosed if these cells have \>= 3 of the following characteristics: CD5+, CD23+, dim surface light chain expression, dim surface CD20 expression, AND FISH analysis is negative for IGH/CCND1 and/or immunostaining is negative for cyclin D1 expression to exclude mantle cell lymphoma Previous treatment for CLL Progressive disease: symptomatic CLL (weight loss\>10% within 6 months, extreme fatigue, fevers\>38.5 C, drenching night sweats without evidence of infection) OR evidence of progressive bone marrow failure (hemoglobin\<11g/dL, platelet count\<100 x 10\^9/L) OR massive (\>6 cm below left costal margin) or progressive palpable splenomegaly OR massive (\>10 cm) or measurable and progressive lymphadenopathy
* Please contact study investigator and/or consult protocol document for specific details on laboratory criteria CD52 expression by CLL cells Willing to provide mandatory biospecimen samples for research studies as required by the protocol Negative serum pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only Willingness to return to the enrolling institution for follow-up
* ECOG Performance Status (PS) 0, 1, or 2--Exceptions: Grade 3 allowed if caused by CLL and not other co-morbidities Provide informed written consent Life expectancy \>= 3 months

Exclusion

* Any of the following comorbid conditions: NYHA class III-IV heart disease, recent myocardial infarction (\< 6 months prior to registration), uncontrolled infection, infection with the human immunodeficiency virus (HIV/AIDS), serological evidence of active hepatitis B infection (HBsAg or HBeAg positive) or positive hepatitis C serology, as further severe immunosuppression with this regimen may occur
* Evidence of active autoimmune hemolytic anemia, immune thrombocytopenia, or pure red blood cell aplasia Other active primary malignancy requiring treatment or that limits survival to =\< 2 years Any major surgery =\< 4 weeks prior to registration Concurrent investigational drug therapy Any of the following: pregnant women,nursing women, men or women of childbearing potential who are unwilling to employ adequate contraception (condoms, diaphragm, birth control pills, injections, intrauterine device \[IUD\], surgical sterilization, abstinence, etc.)
* Concomitant use of the following CYP3A4 strong inhibitors: Clarithromycin, Nefazodone, Telithromycin, Aprepitant, Indinavir, Nelfinavir, Diltiazem, Borisonazole, Itrazonazole, Ritonavir, Erythromycin, Ketoconazole, Saquinavir, Fluconazole (may be used if drug levels can be monitored)
* Patients with any known bleeding diathesis (any congenital bleeding disorder that affects platelet function and/or coagulation including von Willebrand's Disease)
* Severely impaired lung function as defined as spirometry and DLCO that is 50% of the normal predicted value and/or O2 saturation that is 88% or less at rest on room air Receiving anticoagulant therapy