Inclusion Criteria:

          -  Has histologically or cytologically documented relapsed, or refractory pediatric solid
             malignancy excluding osteosarcoma

          -  Has measurable disease as defined by Response Evaluation Criteria In Solid Tumors
             version 1.1 (RECIST 1.1) or Response Assessment in Neuro-Oncology (RANO) for High
             Grade Glioma (HGG)

          -  Has a performance status defined as follows: 1) Lansky Play Score ≥50 for participants
             up to and including 16 years of age 2) Karnofsky performance status (KPS) ≥50 for
             participants >16 years of age 3) Neurologic deficits in participants with primary
             central nervous system (CNS) tumors must have been stable for at least 7 days prior to
             study enrollment

          -  Demonstrate adequate organ function

          -  No clinical evidence of nephrotic syndrome.

          -  Has adequate blood pressure (BP) control with or without antihypertensive medications

          -  Has adequate cardiac function

          -  Has adequate neurologic function

          -  Participant must have fully recovered to Common Terminology Criteria for Adverse
             Events, Version 5.0 (CTCAE v5.0) Grade ≤1 (except for alopecia, ototoxicity, and Grade
             ≤2 peripheral neuropathy) from the acute toxic effects of all prior anticancer therapy

          -  Male participants must agree to use approved contraception during the treatment period
             and for at least 7 days after the last dose of study intervention and refrain from
             donating sperm during this period

          -  Female participants are not pregnant and not breastfeeding, and are not a woman of
             childbearing potential (WOCBP) or are a WOCBP who agrees to follow contraceptive
             guidance during the treatment period and for at least 30 days after the last dose of
             study intervention

        Exclusion Criteria:

          -  Has had major surgery within 3 weeks prior to Cycle 1 Day 1 (C1D1)

          -  Has gastrointestinal (GI) bleeding or active hemoptysis (bright red blood of at least
             half teaspoon) within 21 days prior to enrollment

          -  Has CNS tumors with a history of symptomatic tumor hemorrhage

          -  Has evidence of new intracranial hemorrhage of more than punctate size on MRI
             assessment obtained within 28 days prior to study enrollment

          -  Has radiographic evidence of encasement or invasion of a major blood vessel or of
             intratumoral cavitation

          -  Has evidence of untreated CNS metastases (exception: participants with primary CNS
             tumors and leptomeningeal disease.

          -  Has GI malabsorption, GI anastomosis, or any other condition that in the opinion of
             the investigator might affect the absorption of lenvatinib

          -  Has preexisting ≥Grade 3 GI or non-GI fistula

          -  Has any active infection requiring systemic therapy

          -  Known to be Human immunodeficiency virus (HIV) positive

          -  Known active viral hepatitis (B or C) as demonstrated by positive serology. Testing
             for hepatitis B or hepatitis C is required at screening only when mandated by local
             health authority

          -  Is currently participating and receiving study therapy, or has participated in a study
             of an investigational agent and received study therapy or used an investigational
             device within 4 weeks of the date of allocation

          -  Has a history or current evidence of any condition, therapy, or laboratory abnormality
             that might confound the results of the study, interfere with the participant's
             participation for the full duration of the study, or is not in the best interest of
             the participant to participate, in the opinion of the treating investigator

          -  Has known hypersensitivity to any component of the investigational product (lenvatinib
             or ingredients)

          -  Has known psychiatric or substance abuse disorders that would interfere with
             cooperation with the requirements of the stud

          -  Has clinically significant cardiovascular disease within 6 months from first dose of
             study intervention, including New York Heart Association Class III or IV congestive
             heart failure, unstable angina, myocardial infarction, cerebral vascular accident, or
             cardiac arrhythmia associated with hemodynamic instability

          -  Has non-healing wound, tumor ulceration, unhealed or incompletely healed fracture, or
             a compound (open) bone fracture at the time of enrollment