Lenalidomide in Treating Young Patients With Relapsed or Refractory Solid Tumors or Myelodysplastic Syndromes

Inclusion Criteria:

* Diagnosis of 1 of the following:

  * Histologically confirmed solid tumor

    * No brain tumors
  * Myelodysplastic syndromes (MDS)

    * No refractory anemia with excess blasts in transformation or other forms of acute myeloid leukemia (AML)
    * No FAB diagnosis of refractory anemia with excess blasts in transition and other forms of AML
    * Newly diagnosed MDS with chromosome 5q abnormalities
* Relapsed or refractory disease including relapse after stem cell transplantation
* Measurable or evaluable disease (solid tumor patients only)
* No known curative or life-prolonging therapy exists
* No bone marrow involvement by tumor (solid tumor patients only)
* No CNS tumors
* Performance status - Karnofsky 50-100% (for patients \> 10 years of age)
* Performance status - Lansky 50-100% (for patients ≤ 10 years of age)
* Absolute neutrophil count ≥ 1,000/mm\^3 (for patients with solid tumors)
* Platelet count ≥ 100,000/mm\^3 (30,000 for patients with MDS)

  * Only patients with MDS may receive transfusions to support platelet counts
* Hemoglobin ≥ 8.0 g/dL (transfusions allowed)
* Bilirubin ≤ 1.5 times upper limit of normal (ULN)
* ALT ≤ 110\*
* Albumin ≥ 2 g/dL
* Creatinine clearance OR radioisotope glomerular filtration rate ≥ 70 mL/min
* Creatinine based on age as follows:

  * Creatinine ≤ 0.8 mg/dL (for patients ≤ 5 years of age)
  * Creatinine ≤ 1 mg/dL (for patients 6 to 10 years of age)
  * Creatinine ≤ 1.2 mg/dL (for patients 11 to 15 years of age)
  * Creatinine ≤ 1.5 mg/dL (for patients over 15 years of age)
* No parent or sibling with a known history of venous thrombosis before the age of 50 OR arterial thrombosis before the age of 40
* No thromboembolic event except catheter-related thrombosis
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective double-method contraception 4 weeks before, during, and for ≥ 4 weeks after completion of study treatment
* Body surface area ≥ 0.4m\^2
* No uncontrolled infection
* No active graft-vs-host disease from prior stem cell transplant or rescue
* Recovered from prior immunotherapy
* At least 1 week since prior biologic agents
* At least 1 week since prior hematologic growth factors (2 weeks for pegfilgrastim)
* At least 3 months since prior stem cell transplant or rescue (without total body irradiation \[TBI\])
* Prior thalidomide allowed
* No other concurrent immunotherapy
* No other concurrent biologic therapy
* More than 3 weeks since prior myelosuppressive chemotherapy (6 weeks for nitrosoureas) and recovered
* No concurrent chemotherapy
* Concurrent dexamethasone allowed provided the dose has been either decreasing or stable for the past 7 days
* See Biologic therapy
* Recovered from prior radiotherapy
* At least 2 weeks since prior local palliative (small port) radiotherapy
* At least 6 months since prior TBI, craniospinal radiotherapy, or radiotherapy to ≥ 50% of the pelvis
* At least 6 weeks since other prior substantial bone marrow radiotherapy
* No concurrent radiotherapy
* No other concurrent investigational drugs or agents
* No other concurrent anticancer agents