Lenalidomide in Treating Young Patients With Recurrent, Progressive, or Refractory CNS Tumors

Inclusion Criteria: * Patients with a histological diagnosis of a primary CNS tumor (including histologically benign brain tumors (e.g. low-grade glioma) that is recurrent, progressive, or refractory to standard therapy; patients with intrinsic brain stem or diffuse optic pathway tumors do not require histological confirmation of disease but should have clinical and/or radiographic evidence of progression * Karnofsky Performance Scale (KPS for \>= 16 yrs of age) or Lansky Performance Score (LPS for ≤ 16 years of age) ≥ 60 assessed within two weeks prior to registration * Patient must be able to swallow capsules * Patients must have recovered from any significant acute toxicity associated with prior therapy; patients must have no known curative therapy available; patients will be eligible regardless of the number of prior therapies, as long as other eligibility criteria are met * Chemo: Prior use of thalidomide is acceptable; patients must have: * Received their last dose of known myelosuppressive anticancer chemotherapy or biological therapy at least three (3) weeks prior to study registration * Received their last dose of nitrosourea or mitomycin-C at least six (6) weeks prior to study registration * Received their last dose of other investigational agent or an anticancer drug known to not be myelosuppressive at least seven (7) days prior to study registration * XRT: Patients must have had their last fraction of craniospinal irradiation ≥ 3 months prior to registration and their last fraction of local irradiation to primary tumor ≥ 4 weeks prior to registration * Bone Marrow Transplant: ≥ 6 months since allogeneic bone marrow transplant and ≥ 3 months since autologous bone marrow/stem cell prior to registration * Growth factors: Off all colony forming growth factor(s) \> 2 weeks prior to registration (filgrastim, sargramostim, erythropoietin) * The following laboratory values must be assessed within two (2) weeks prior to registration and again within seven (7) days prior to the start of therapy; laboratory tests should be repeated within 48 hours of beginning therapy if there has been a significant clinical change * Absolute neutrophil count ≥ 1000/μl (unsupported) * Platelets ≥ 100,000/μl (unsupported) * Hemoglobin ≥ 8.0 g/dL (may be supported) * Serum creatinine within upper limit of institutional normal for age * Or GFR ≥ 70 ml/min/1.73m\^2 * Bilirubin ≤ 1.5 times upper limit of normal for age * SGPT (ALT) ≤ 2.5x institutional upper limit of normal for age * Albumin ≥ 2 g/dL * No overt renal, hepatic, cardiac or pulmonary disease * Female patients of childbearing potential must have negative serum or urine pregnancy test (sensitivity of at least 50mIU/ml); patients must not be pregnant or breast-feeding * All sexually active females must begin 2 methods of birth control, including 1 highly effective method, and 1 additional method (at the same time) at least 4 weeks prior to the first dose of CC-5013; this applies to all sexually active females of childbearing potential unless they have not had a menstrual period in 2 years or have undergone a hysterectomy * Patients of child fathering potential must agree to use latex condoms during intercourse with a woman while taking CC-5013 and for 4 weeks thereafter * Signed informed consent according to institutional guidelines must be obtained Exclusion Criteria: * Patients with a body surface area (BSA) ≤ 0.4 m\^2 are excluded * Patients with a first-degree relative with a history of venous thrombosis before age 50 yrs or an arterial thrombosis before age 40 yrs are excluded * Patients who have had a thromboembolic event that is not line-related are excluded * Patients with any significant medical illnesses that, in the investigator's opinion, cannot be adequately controlled with appropriate therapy or would compromise a patient's ability to tolerate this therapy * Patients with any disease that would obscure toxicity or dangerously alter drug metabolism * Patients receiving any other chemotherapeutics or investigational agents * Patients with uncontrolled infection * Patients unable to swallow capsules * Patients with known hypersensitivity to anhydrous lactose, microcrystalline cellulose, croscarmellose sodium, and magnesium stearate