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