A Study to Compare the Efficacy and Safety of Ifosfamide and Etoposide With or Without Lenvatinib in Children, Adolescents and Young Adults With Relapsed and Refractory Osteosarcoma

Inclusion Criteria:

1. Histologically or cytologically confirmed diagnosis of high grade osteosarcoma
2. Refractory or relapsed osteosarcoma after 1 to 2 prior lines of systemic treatments
3. Measurable or evaluable disease per RECIST 1.1.
4. Life expectancy of 12 weeks or more
5. Lansky play score greater than or equal to (\>=) 50 Percent (%) or Karnofsky Performance Status score \>=50%. Use Karnofsky for participants \>=16 years of age and Lansky for participants less than (\<)16 years of age. Participants who are unable to walk because of paralysis, but who are able to perform activities of daily living while wheelchair bound, will be considered ambulatory for the purpose of assessing the performance score
6. Adequate organ function per blood work
7. Adequate cardiac function as evidenced by left ventricular ejection fraction (LVEF) \>=50% at baseline as determined by echocardiography or multigated acquisition (MUGA) scan
8. Adequately controlled blood pressure (BP) with or without antihypertensive medications, defined as:

   BP \<95th percentile for sex, age, and height/length at screening (as per National Heart Lung and Blood Institute guidelines) and no change in antihypertensive medications within 1 week prior to Cycle 1 Day 1. Participants \>18 years of age should have BP less than or equal to (\<=) 150/90 millimeters of Mercury at screening and no change in antihypertensive therapy within 1 week prior to Cycle 1 Day 1
9. Washout before Cycle 1 Day 1 of 3 weeks in case of prior chemotherapy, 6 weeks if treatment included nitrosoureas; 4 weeks for definitive radiotherapy, 2 weeks for palliative radiotherapy; and 3 months from high-dose chemotherapy and stem cell rescue. For all other anti-cancer therapies, washout before Cycle 1 Day 1 of at least 5 half-lives (or at least 28 days, whichever is shorter). Participants must have recovered \[to Grade \<=1, except for alopecia, ototoxicity, and Grade \<=2 peripheral neuropathy, per common terminology criteria for adverse events (CTCAE) v5.0\] from the acute toxic effects of all prior anticancer therapy before Cycle 1 Day 1
10. Must have no prior history of lenvatinib treatment

Eligibility for optional lenvatinib crossover:

1. Disease progression per RECIST 1.1 (as confirmed by IIR for all participants who crossover prior to the study data-cut)
2. No new systemic anti-cancer medication administered after the last dose of study drugs
3. Meets all safety parameters listed in the inclusion criteria and none listed in the exclusion criteria
4. Study is ongoing

Exclusion Criteria:

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