CCI-779 in Treating Patients With Recurrent or Refractory B-Cell Non-Hodgkin's Lymphoma or Chronic Lymphocytic Leukemia

Inclusion Criteria: * Histologically or cytologically confirmed B-cell non-Hodgkin's lymphoma, including the following subtypes: * Aggressive B-cell lymphoma (Group A) * Diffuse large B-cell lymphoma * Transformed lymphoma * Follicular lymphoma (Group B) * Small lymphocytic lymphoma * Chronic lymphocytic leukemia (CLL) (Group C) * Other B-cell small lymphocytic disorders * No mantle cell lymphoma * No potentially curative treatment options because of lack of response, relapse, or ineligibility * Relapsed or refractory disease * Patients with refractory disease (i.e., less than a partial response to the last treatment) must have received no more than 3 prior regimens (group A) * Patients with sensitive disease (i.e., at least a partial response to the last treatment) must have received no more than 4 prior regimens (group A) * Patients who have failed prior autologous transplantation are eligible (group A) * No more than 5 prior regimens (groups B and C) * The salvage regimen, conditioning regimen, and any maintenance therapy are considered 1 regimen * Prior rituximab or alemtuzumab is not considered prior therapy * No limitation to the amount of prior radiotherapy * No CNS involvement * Performance status: ECOG 0-2 OR Karnofsky 60-100% * Life expectancy more than 3 months * No symptomatic congestive heart failure * No unstable angina pectoris * No cardiac arrhythmia * No prior allergic reactions attributed to compounds of similar chemical or biological composition to CCI-779 * No ongoing or active infection * No psychiatric illness or social situation that would preclude study compliance * No other active malignancy except nonmelanoma skin cancer or carcinoma in situ of the cervix Completed therapy and considered \< 30% risk of relapse * No other concurrent uncontrolled illness * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No concurrent prophylactic hematopoietic colony-stimulating factors * No concurrent pegfilgrastim * More than 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin) and recovered * More than 4 weeks since prior radiotherapy and recovered * No concurrent combination antiretroviral therapy for HIV-positive patients * No concurrent unconventional therapies, food, or vitamin supplements containing Hypericum perforatum (St. John's wort) * No other concurrent known inducers of CYP3A4 * No other concurrent investigational agents * No other concurrent anticancer therapy * Measurable disease\* * At least 1 unidimensionally measurable lesion \>= 20 mm by conventional techniques OR \>= 10 mm by spiral CT scan \[Note: \*Only bone marrow or peripheral blood involvement required for CLL and Waldenstrom's macroglobulinemia \] * Absolute neutrophil count \>= 1,000/mm3 * Bilirubin =\< 1.5 times upper limit of normal (ULN) * AST and ALT =\< 2.5 times ULN * Creatinine =\< 1.5 times ULN * Fasting cholesterol =\< 350 mg/dL * Fasting triglycerides =\< 400 mg/dL * Platelet count \>= 50, 000/mm3 (\> 20,000/mm3 for patients with thrombocytopenia due to bone marrow involvement)