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)