Low-Dose or High-Dose Lenalidomide in Treating Younger Patients With Recurrent, Refractory, or Progressive Pilocytic Astrocytoma or Optic Pathway Glioma

Inclusion Criteria: * Patients must have a body surface area (BSA) \>= 0.4 m\^2 at the time of study enrollment * Patients must have a pilocytic astrocytoma or optic pathway glioma that has relapsed, progressed, or become refractory to conventional therapy; patients with neurofibromatosis (NF-1) are eligible * Patients must have histologic verification of malignancy; histologic confirmation for patients with optic pathway gliomas will not be required * Patients must have measurable residual disease, defined as tumor that is measurable in two perpendicular diameters on magnetic resonance imaging (MRI); for a lesion to be considered measurable, it must be at least twice the slice thickness on MRI (i.e. visible on more than one slice) * To document the degree of residual tumor, the following must be obtained: * All patients must have a brain MRI with and without contrast (gadolinium) within 1 week prior to study enrollment; for patients on steroids, baseline MRI scans must be performed after at least 1 week at a stable or decreasing dose of steroids * All patients with a history of spinal or leptomeningeal disease, and those patients with symptoms suspicious of spinal disease, must have a spine MRI with and without contrast (gadolinium) performed within 2 weeks prior to study enrollment * Patients must have a Lansky or Karnofsky performance status score of \>= 60%; use Karnofsky for patients \> 16 years of age and Lansky for patients =\< 16 years of age * Patients must have been treated with at least one prior treatment regimen that included carboplatin; patients who have received prior radiation therapy for this tumor are eligible * Patients must have recovered (to Common Toxicity Criteria \[CTC\] version \[v.\]4.0 =\< grade 1 unless indicated below) from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study, with the exception of alopecia, weight changes and grade I or II lymphopenia * Myelosuppressive chemotherapy: must not have received within 3 weeks of entry onto this study (6 weeks if prior nitrosourea or mitomycin-C) * Biologic (anti-neoplastic agent): at least 7 days after the last dose of a biologic agent; for agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur * Immunotherapy: at least 42 days after the completion of any type of immunotherapy, e.g. tumor vaccines * Monoclonal antibodies: at least 3 half-lives of the antibody after the last dose of a monoclonal antibody * Radiation therapy (RT): patients must have had their last fraction of craniospinal RT \>= 6 months prior to study entry and their last fraction of focal RT \>= 4 weeks prior to study entry; if the lesion used for on-study criteria is in the radiation field, there must be evidence of tumor progression after radiation therapy was completed * Study specific limitations on prior therapy: * Patients who have received thalidomide are eligible if all acute thalidomide-related toxicity has resolved * Patients must not have received lenalidomide previously * Growth factor(s): must not have received within 2 weeks of entry onto this study * Steroids: patients who are receiving corticosteroids must be on a stable or decreasing dose for at least 1 week prior to baseline MRI * Peripheral absolute neutrophil count (ANC) \>= 1,000/uL * Platelet count \>= 100,000/uL (transfusion independent) * Hemoglobin \>= 8.0 g/dL (may receive red blood cell \[RBC\] transfusions) * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 mL/min/m\^2 OR a serum creatinine based on age/gender as follows: * 0.4 mg/dL (1 month to \< 6 months of age) * 0.5 mg/dL (6 months to \< 1 year of age) * 0.6 mg/dL (1 to \< 2 years of age) * 0.8 mg/dL (2 to \< 6 years of age) * 1.0 mg/dL (6 to 10 years of age) * 1.2 mg/dL (10 to \< 13 years of age) * 1.5 mg/dL (male) or 1.4 mg/dL (female) (13 to \< 16 years of age) * 1.7 mg/dL (male) or 1.4 mg/dL (female) (\>= 16 years of age) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) for age * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 110 U/L; for the purpose of this study, the ULN for SGPT is 45 U/L * Serum albumin \>= 2 g/dL * No evidence of dyspnea at rest and a pulse oximetry \> 94% if there is clinical indication for determination * Patients must be able to swallow intact capsules * All patients and/or their parents or legal guardians must sign a written informed consent * All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met Exclusion Criteria: * Female patients who are pregnant are not eligible * Lactating females are not eligible unless they have agreed not to breastfeed their infants while receiving protocol therapy and for 28 days after the last dose of lenalidomide * Female patients of childbearing potential are not eligible unless they commit to complete abstinence or have been on 2 methods of birth control, including 1 highly effective method and 1 additional method at the same time (unless committing to complete abstinence of heterosexual intercourse) at least 28 days (4 weeks) prior to study enrollment; sexually active females must also agree to remain on 2 methods of birth control, during treatment (including during dose interruptions), and continuing for at least 28 days after the completion of protocol therapy; examples of methods of contraception are as follows: * Highly effective methods (must use at least 1): * Intrauterine device (IUD) * Hormonal (prescription birth control pills, injections, implants) * Tubal ligation * Partner's vasectomy * Additional effective methods: * Male condom * Diaphragm * Cervical cap The two methods of birth control requirement applies to all sexually active females unless they have undergone a hysterectomy or bilateral oophorectomy * Female patients of childbearing potential (including those who commit to complete abstinence) are not eligible unless they agree to ongoing pregnancy testing and counseling every 28 days about pregnancy precautions and risks of fetal exposure * Male patients of child fathering potential are not eligible unless they have agreed to use latex condoms during intercourse with a woman of childbearing potential while receiving treatment and for 28 days thereafter * Patients with a history of thromboembolism unrelated to a central line, or patients with a known predisposition syndrome for thromboembolism are not eligible * Patients who have an uncontrolled or untreated infection are not eligible * Patients with known overt cardiac disease, including but not limited to a history of myocardial infarction, severe or unstable angina, clinically significant peripheral vascular disease, grade 2 or greater heart failure, or serious and inadequately controlled cardiac arrhythmia are not eligible * Patients with a significant systemic illness that is not well-controlled in the opinion of the treating physician are not eligible