Inclusion Criteria:  Age: At time of study enrollment, patients must be  Part 1 (including PK expansion cohort): ≥2 and ≤21 years of age; Part 2: ≥2 and ≤21 years of age; Patients with osteosarcoma can enroll up to <30 years old.  Diagnosis:  Part 1 - Patients with any recurrent or refractory solid tumors or lymphoma (not central nervous system [CNS]) that have a known or expected dysfunction of VEGFR 1, -2, and -3; FGFR-1, or CSF-1R pathways (based on literature) are eligible. Patients must have had histologic verification of malignancy at original diagnosis or relapse. Part 2 - Recurrent or refractory osteosarcoma (US and EU), Ewing sarcoma (US and EU), RMS (US and EU), or NRSTS (EU only). Patients must have had histologic verification of malignancy at original diagnosis or relapse. Disease status: Patients must have measureable or evaluable disease for part 1 dose escalation; for part 2, patients must have measurable disease by RECIST version 1.1. Therapeutic options: Patient's current disease state must be one for which there is no known curative therapy. Performance level: Karnofsky ≥50 for patients ≥16 and <18 years of age and Lansky ≥50 for patients <16 years of age, Eastern Cooperative Oncology Group (ECOG) ≤2 for patients ≥18 years of age. Adequate organ and bone marrow function as defined in the current protocol. Adequate cardiac function as indicated as defined in the current protocol. Patients with known bone marrow metastatic disease will be eligible for the study provided they meet the blood counts in the inclusion criteria as defined in the current protocol. Adequate BP control which is defined as a BP <95th percentile (≤ grade 1) for age, height, and sex. Informed consent: Provision of signed and dated written informed consent (parent/legal guardian if patient <18 years of age) and assent (from patients aged >7 years) prior to any study-specific procedures, sampling, and analyses. Patient must meet all defined Inclusion criteria as defined in the current protocol.  Exclusion Criteria:  Patient must not meet any exclusion criteria as defined in the current protocol. Pregnant, breast feeding or planning on becoming pregnant. Patients is taking and prohibitive concomitant medications as outlined in the current protocol. Patients have an uncontrolled infection. Patients has had major surgery or significant traumatic injury within 28 days of the first dose. Brain metastases and/or spinal cord compression untreated with surgery and/or radiotherapy and without clinical imaging evidence of SD for 14 days or longer. History of allergies to Surufatinib and/or Gemcitabine.