Multicentre Placebo-controlled Double-blinded Phase II Study of Lenvatinib Efficacy in Patients With Locally Advanced or Metastatic GIST (Gastrointestinal Stromal Tumor) After Imatinib/Sunitinib Failure

Inclusion Criteria: I1. Male or female ≥ 18 years at the day of consenting to the study. I2. Patient must have histologically confirmed diagnosis of GIST. I3. Disease must be locally advanced or metastatic. I4. Patient who failed (disease progression and/or intolerance) previously at least to imatinib and sunitinib. Nota Bene: patients with more than 2 previous anticancer treatments are eligible. I5. Patient must have evidence of measurable disease as per the RECIST version 1.1 (Appendix 2). I6. Patient must have documented disease progression. I7. ECOG performance status 0, 1 or 2 (Appendix 3). I8. Patient must have normal organ and bone marrow function as defined below: * Hematologic * Absolute neutrophil count (ANC) ≥ 1.5 Gi/L * Haemoglobin ≥ 9 g/dl (5.6 mmol/l) (subjects may not have had a transfusion within 7 days of screening assessment) * Platelets ≥ 100 Gi/l * Coagulation panel * Prothrombin time (PT) or international normalized ratio (INR) ≤ 1.2 X upper limit of normal (ULN) * Partial thromboplastin time (PTT) ≤ 1.2 X ULN Subjects receiving anticoagulant therapy are eligible if their INR is stable and within the recommended range for the desired level of anticoagulation. * Hepatic * Total bilirubin ≤ 1.5 X ULN * AST and ALT ≤ 2.5 X ULN * Renal * Serum creatinine ≤ 1.5 mg/dl (133 µmol/l) Or, if greater than 1.5 mg/dl: calculated creatinine clearance ≥ 50 ml/min * Urine Protein to Creatinine ratio (UPC) \< 1; If UPC \> 1, then a 24-hour urine protein must be assessed. Subjects must have a 24-hour urine protein value \<1g. I9. Patient and his/her partner using an effective contraception as defined in Appendix 1. I10. Patient able to understand and willingness for follow-up visits. I11. Patient covered by a medical insurance. I12. Signed and dated informed consent document indicating that the patient has been informed of all the pertinent aspects of the trial prior to any study-specific procedure. Exclusion Criteria: E1. Patient with a documented mutation in PDGFRA exon 18 (D842V substitution). E2. Clinically significant gastrointestinal abnormalities that may increase the risk for gastrointestinal bleeding including, but not limited to: * Active peptic ulcer disease * Known intraluminal metastatic lesions with risk of bleeding * Inflammatory bowel disease (e.g. ulcerative colitis, Crohn's disease), or other gastrointestinal conditions with increased risk of perforation * History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 28 days prior to beginning study treatment * Clinically significant gastrointestinal abnormalities that may affect absorption of investigational product including, but not limited to: * Malabsorption syndrome * Major resection of the stomach or small bowel. E3. Any active/uncontrolled infection, including known infection with HIV, Hepatitis B or Hepatitis C. E4. Corrected QT interval (QTc) \> 480 msecs using Bazett's formula E5. History of any one or more of the following cardiovascular conditions within the past 6 months prior to the first dose of study drug: * Cardiac angioplasty or stenting * Myocardial infarction * Unstable angina * Coronary artery bypass graft surgery * Symptomatic peripheral vascular disease * Class III or IV congestive heart failure, as defined by the New York Heart Association (NYHA) classification. E6. Poorly controlled arterial hypertension (Systolic blood pressure: 150mmHg / Diastolic blood pressure: 90mmHg). Note: Patients with high blood pressure can be enrolled provided that the hypertension is well controlled at a stable dose of antihypertensive therapy for at least 1 week prior to lenvatinib start). E7. Prior major surgery or trauma within 28 days prior to first dose of study drug and/or presence of any non-healing wound, fracture, or ulcer (procedures such as catheter placement not considered to be major). E8. Evidence of active bleeding or bleeding diathesis. E9. Known endobronchial lesions and/or lesions infiltrating major pulmonary vessels. E10. Clinically significant haemoptysis within 8 weeks of first dose of study drug. E11. Any serious and/or unstable pre-existing medical, psychiatric, or other condition (geographic, social…) that could interfere with subject's safety, provision of informed consent, or compliance to study procedures. E12. Unable or unwilling to discontinue use of prohibited medications list in Section 6.3 for at least 14 days or five half-lives of a drug (whichever is longer) prior to the first dose of study drug and for the duration of the study. E13. Any ongoing toxicity from prior anti-cancer therapy that is \> Grade 1 and/or that is progressing in severity, except alopecia. E14. Inability to swallow E15. Any contraindication to Lenvima®, according to its Summary of Product Characteristics E16. History of hypersensitivity or allergic reactions attributed to compounds of similar chemical or biologic composition of lenvatinib E17. Clinically significant unrelated systemic illness (e.g., serious infection or significant cardiac, pulmonary, hepatic, or other organ dysfunction) that would compromise the patient's ability to tolerate study treatment or would likely interfere with study procedures or results. E18. Pregnant or breastfeeding women. Women of childbearing potential (Appendix 1) are required to have a negative serum pregnancy test within 72 hours prior to study treatment start. A positive urine test must be confirmed by a serum pregnancy test Note: Female if applicable, subjects should discontinue breast-feeding prior to the first dose of study drug and should refrain from breastfeeding throughout the treatment period and for 14 days following the last dose of study drug. E19. Patient under tutorship or curatorship.