Lenvatinib and Eribulin in Advanced Soft Tissue Sarcoma

Inclusion criteria 1. A histological confirmed adipocytic sarcoma (dedifferentiated, myxoid, or pleomorphic) or leiomyosarcoma that is either inoperable locally advanced or metastatic 2. Advanced adipocytic sarcoma and leiomyosarcoma who have received no more than 2 lines of systemic chemotherapy in the advanced setting (not including adjuvant chemotherapy). 3. At least one measurable tumor according to RECIST 1.1. If the measurable lesion has previously received radiotherapy, the tumor must be a progressive lesion after radiotherapy. 4. ECOG PS 0 or 1 or Karnofsky performance status (KPS) ≥ 70 5. Patients must have adequate organ function and marrow reserve measured within 14 days prior to randomization as defined below: * Hemoglobin ≥ 9.0 g/dL; * Absolute neutrophil count ≥ 1,500 /µL; * Platelets ≥ 75,000/µL; * Total bilirubin ≤ 1.5 x upper normal limit; * aspartate aminotransferase (AST)/ alanine aminotransferase (ALT) ≤ 2.5 x upper normal limit; for patients with liver metastases AST(SGOT)/ALT(SGPT) ≤ 5 x upper normal limit is allowed; * Serum creatinine ≤ 1.5mg/dL or creatinine clearance ≥ 50ml/min; * activated partial thromboplastin time (aPTT) \< 1.5 x upper normal limit (unless on therapeutic anti-coagulation); * Proteinuria ≤ 1+ with urine dipstick, if \> 1+, 24-hour urine protein must be ≤ 1 g 6. Age 20 or older. 7. Patient's life expectancy is more than 3 months 8. All women of childbearing potential must have a negative pregnancy test obtained within 72 hours before starting therapy. 9. Patients with reproductive potential must use effective contraception (hormone or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 6 months after the completion of therapy. 10. Patient needs to have adequate wash-out period from previous systemic treatment(s): (1) 2 weeks for any other oral anti-cancer targeted agents (2) 3 weeks for any other cytotoxic chemotherapy (except for mitomycin-C, which will require 6 weeks) (3) 3 weeks for monoclonal antibodies, including immune checkpoint inhibitors Exclusion criteria 1. Patients who had received lenvatinib or eribulin treatment 2. Patients who had leptomeningeal metastasis, either diagnosed by brain imaging study or confirmed by cerebrospinal fluid cytology examination (patients with brain metastasis that are under control is eligible). 3. Patients with clinical signs or symptoms of gastrointestinal obstruction and who require parenteral hydration and/or nutrition because of obstruction. 4. Patients with uncontrollable hypertension (defined as systolic blood pressure over 140mmHg and/or diastolic pressure over 90mmHg despite anti-hypertensive medications) 5. Patients with the following cardiac disease * Prolongation of corrected QT (QTc) interval to \>480 milliseconds (ms). * Significant cardiovascular impairment: history of (a) congestive heart failure greater than New York Heart Association (NYHA) Class II; (b) unstable angina; (c) myocardial infarction; (d) stroke; or (e) cardiac arrhythmia associated with hemodynamic instability within 6 months of the first dose of study drugs. 6. Bleeding subjects at risk for severe hemorrhage. 7. Arterial thromboembolic event within the past 6 months, including transient ischemic attack, cerebrovascular accident, unstable angina, or myocardial infarction. 8. Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to enrollment. 9. History of allergic reaction to compounds of similar chemical composition to the study drugs 10. Pregnancy or lactation.