Additional Study Information: This is a Phase 1/2 multicenter study of lenvatinib administered in combination with everolimus inpediatric patients with relapsed or refractory solid tumors, including CNS tumors. The study treatment is considered experimental because lenvatinib is not approved by the United States(US) Food and Drug Administration (FDA) for treating pediatric patients with refractory solid tumors, including CNS tumors. The purpose of this study is to determine the highest safe dose of lenvatinib administered in combination with everolimus. Another objective is to study the effects of this combination of drugs on the body. Lenvatinib and everolimus will be administered every day orally (by mouth) for 28 days (a treatment cycle is 28 days long). Tests will be done to check the tumor at the end of cycle 1 (week 4), at week 12, week 24, and then every 12 weeks, or as clinically indicated.Blood samples will be collected to determine how much lenvatinib and everolimus is in the blood during the study (pharmacokinetics). Blood and tissue samples will also be collected to determine how genes affect the ability to absorb, distribute, breakdown and get rid of lenvatinib and everolimus from the body. The Phase 1 part of the study is to determine the highest safe dose of lenvatinib administered in combination with everolimus. Once the highest safe dose of the combination of lenvatinib and everolimus has been determined in the Phase 1 part, the Phase 2 portion of this study will open to patients with CNS tumors.