OLIE: This study is comparing the safety and effectiveness of using a form of targeted therapy in combination with chemotherapy for the treatment of children, adolescents, and young adults with Osteosarcoma, rather than using chemotherapy on its ownA Multicenter, Open-label, Randomized Phase 2 Study to Compare the Efficacy and Safety of Lenvatinib in Combination With Ifosfamide and Etoposide Versus Ifosfamide and Etoposide in Children, Adolescents and Young Adults With Relapsed or Refractory Osteosarcoma (OLIE)

Exclusion

1. Any active infection or infectious illness unless fully recovered prior to Cycle 1 Day 1 (that is, no longer requiring systemic treatment)
2. Participants with central nervous system metastases are not eligible, unless they have completed local therapy (example, whole brain radiation therapy, surgery or radiosurgery) and have discontinued the use of corticosteroids for this indication for at least 2 weeks before Cycle 1 Day 1
3. Active second malignancy within 2 years prior to enrollment ([in addition to osteosarcoma], but not including definitively treated superficial melanoma, carcinoma-in-situ, basal or squamous cell carcinoma of the skin)
4. Has had major surgery within 3 weeks prior to Cycle 1 Day 1. Note: Adequate wound healing after major surgery must be assessed clinically, independent of time elapsed for eligibility
5. A clinically significant electrocardiogram (ECG) abnormality, including a marked baseline prolonged QT or corrected QT (QTc) interval (example, a repeated demonstration of a QTc interval greater than [>] 480 millisecond [msec])
6. 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. Note: Medically controlled arrhythmia would be permitted
7. Gastrointestinal malabsorption, gastrointestinal anastomosis, or any other condition that in the opinion of the investigator might affect the absorption of lenvatinib
8. Pre-existing Grade >=3 gastrointestinal or non-gastrointestinal fistula
9. Gastrointestinal bleeding or active hemoptysis (bright red blood of at least 1 divided [/] by 2 teaspoon) within 3 weeks prior to Cycle 1 Day 1
10. Radiographic evidence of intratumoral cavitation, encasement, or invasion of a major blood vessel. Additionally, the degree of proximity to major blood vessels should be considered for exclusion because of the potential risk of severe hemorrhage associated with tumor shrinkage/necrosis after lenvatinib therapy
11. History of ifosfamide-related Grade >=3 nephrotoxicity or encephalopathy
12. Known to be human immunodeficiency virus (HIV) positive
13. Known active Hepatitis B (example, Hepatitis B surface antigen [HBsAg] reactive) or Hepatitis C (example, hepatitis C virus [HCV] ribonucleic acid [RNA] [qualitative] is detected). Note: Testing for Hepatitis B or Hepatitis C is required at screening only when mandated by local health authority