A Study of E7050 in Combination With E7080 in Participants With Advanced Solid Tumors (Dose Escalation) and in Participants With Recurrent Glioblastoma or Unresectable Stage III or Stage IV Melanoma After Prior Systemic Therapy (Expansion Cohort and Phase 2)

Inclusion Criteria: Participants must meet all of the following criteria to be included in this study: 1. Phase 1b: Unresectable advanced or metastatic solid tumors. 2. Phase 1b expansion cohort and Phase 2: Histological confirmed diagnosis of glioblastoma (expansion cohort and Cohort 1) or melanoma (expansion cohort and Cohort 2). Phase 1b expansion cohort glioblastoma participants, Phase 2 Cohort 1: 3. No evidence of active central nervous systems (CNS) hemorrhage on baseline scans other than in those participants with recurrent glioblastoma who are stable Grade 1. 4. Participants having first or second recurrence documented by magnetic resonance imaging (MRI), following primary management with surgical resection or biopsy, radiotherapy and up to two prior systemic treatments. 5. If participants is on corticosteroids, they must be on a stable dose for 1 week prior to first dose of study drug. 6. Measurable disease defined as bidimensionally contrast enhancing lesions with clearly defined margins by computerized tomography (CT) or MRI scan, with a minimal diameter of 1 cm, and visible on two axial slices which are preferably at most 5 millimeter (mm) apart with 0 mm skip. Phase 1b expansion cohort melanoma participants, Phase 2 Cohort 2: 7. Radiographic/ photographic evidence of disease progression according to Response Evaluation Criteria in Solid Tumors (RECIST 1.1) (Appendix 3) after no more than two prior systemic regimens for unresectable Stage III or Stage IV disease. 8. American Joint Committee on Cancer (AJCC) unresectable Stage III or Stage IV melanoma. 9. Measurable disease meeting the following criteria: 1. At least one lesion of greater than or equal to 1.0 cm in the longest diameter for a non-lymph node or greater than or equal to 1.5 centimeter (cm) in the short-axis diameter for a lymph node which is serially measurable according to RECIST 1.1 using CT/MRI or photography. If there is only one target lesion and it is a non-lymph node, it should have a longest diameter of greater than or equal to 1.5 cm. 2. Lesions that have had external beam radiotherapy or loco-regional therapies such as radio frequency ablation must show evidence of progressive disease based on RECIST 1.1 to be deemed a target lesion. All participants: 10. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. 11. Adequately controlled blood pressure (BP) with or without antihypertensive medications, defined as BP less than or equal to 150/90 millimeter of mercury (mmHg) at screening and no change in antihypertensive medications within 1 week before the Screening Visit. 12. Adequate renal function as evidenced by serum creatinine less than or equal to 2.0 milligrams per deciliter (mg/dL) or calculated creatinine clearance greater than or equal to 40 milliliters per minute (mL/min) per the Cockcroft and Gault formula (see Appendix 5). 13. Adequate bone marrow function: * Absolute neutrophil count greater than or equal to 1500/mm3 (greater than or equal to 1.5 x 10\^3/uL); * Platelets greater than or equal to 100,000/mm3 (greater than or equal to 100 x 10\^9/L); * Hemoglobin greater than or equal to 9.0 g/dL. 14.Adequate blood coagulation function, as evidenced by an International Normalized Ratio (INR) less than or equal to 1.5. 14. Adequate liver function: * Bilirubin less than or equal to 1.5 x the upper limit of normal (ULN) except for unconjugated hyperbilirubinemia of Gilbert's syndrome; * ALP, ALT, and AST less than or equal to 3 x ULN (less than or equal to 5 x ULN if participant has liver metastases). 15. Males or females age greater than or equal to 18 years at the time of informed consent. 16. All females must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of beta-human chorionic gonadotropin \[B-hCG\] at the Screening and Baseline Visit (a separate Baseline assessment is not required if a negative Screening pregnancy test was obtained within 72 hours before the first dose of study drug). Females of child-bearing potential, if not practising total abstinence or having a vasectomized partner with confirmed azoospermia, must agree to use two highly effective methods of contraception: e.g., 1) an intrauterine device (IUD) or intrauterine system (IUS); 2) a barrier method such as a condom or occlusive cup (diaphragm or cervical/vault caps) + spermicide (foam, gel, cream, etc.); 3) oral, injected, or implanted hormonal contraceptives throughout the entire study period and for 30 days after study drug discontinuation. Use of a double-barrier method (i.e., use at the same time of a condom + occlusive cup \[diaphragm or cervical/vault caps\] + spermicide \[foam, gel, cream, etc.\]) is accepted as two highly effective methods of contraception. The only participants who will be exempt from this requirement are postmenopausal women (defined as women who have been amenorrheic for at least 12 consecutive months, in the appropriate age group, without other known or suspected primary cause) or participants who have been sterilized surgically or who are otherwise proven sterile (i.e., bilateral tubal ligation with surgery at least 1 month prior to dosing, total hysterectomy, or bilateral oophorectomy with surgery at least 1 month prior to dosing). All women who are of reproductive potential and who are using hormonal contraceptives must have been on a stable dose of the same hormonal contraceptive product for at least 4 weeks prior to dosing and must continue to use the same contraceptive during the study and for 30 days after study drug discontinuation. 17. Male participants who are partners of women of childbearing potential must use a condom + spermicide and their female partners, if of childbearing potential, must use a highly effective method of contraception (see methods described in Inclusion Criterion #18) beginning at least 1 menstrual cycle prior to starting study drug, throughout the entire study period, and for 30 days after the last dose of study drug, unless the male participants are totally abstinent sexually or have undergone a successful vasectomy with confirmed azoospermia or unless the female partners have been sterilized surgically or are otherwise proven sterile (see Inclusion Criterion #16). 18. Voluntary agreement to provide written informed consent and the willingness and ability to comply with all aspects of the protocol. Exclusion Criteria: Participants who meet any of the following criteria will be excluded from this study: 1. Phase 1b Dose Escalation: Participants who discontinued prior TK inhibitor (including VEGFR and c-Met receptor targeted therapy) due to toxicity will be ineligible. 2. Phase 1b Dose Escalation (3+3 portion) participants with primary CNS tumors 3. Phase 1b Dose Escalation participants, melanoma participants in expansion cohort and Phase 2 Cohort 2: Participants with untreated or unstable metastases to the central nervous system (CNS) are excluded. participants who have completed local therapy and have discontinued the use of steroids for this indication at least 4 weeks prior to commencing treatment and have remained asymptomatic for at least 4 weeks prior to commencing treatment are eligible. 4. Phase 2: Prior exposure to VEGF-targeted treatment or c-Met or hepatocyte growth factor (HGF) targeted treatment. 5. Phase 2: Active malignancy (except for glioblastoma (Cohort 1) or unresectable Stage III or Stage IV melanoma (Cohort 2); or melanoma in situ, basal or squamous cell carcinoma of the skin, or carcinoma in situ of the cervix) within the past 24 months. Phase 1b expansion cohort glioblastoma participants and Phase 2 Cohort 1: 6. More than two recurrences of glioblastoma. 7. Prior bevacizumab treatment. 8. Surgical resection of brain tumor within 4 weeks, or prior stereotactic biopsy within 2 weeks of Screening visit. 9. Prior radiotherapy within 12 weeks unless there is a new area of enhancement consistent with recurrent tumor outside of the radiation field (beyond the high dose region or 80% isodose line), or there is biopsy-proven unequivocal viable tumor on histopathology sampling (e.g., "solid" tumor areas (i.e. greater than 70% tumor cell nuclei in areas), high or progressive increase in MIB-1 proliferation index compared to prior biopsy, or evidence for histological progression or increased anaplasia in the tumor). 10. Participants who have received enzyme-inducing anti epileptic agents within 14 days before the first dose of study drug (e.g., carbamazepine, phenytoin, phenobarbital, primidone, or oxcarbazepine). Phase 1b expansion cohort participants with melanoma and Phase 2 Cohort 2: 11. More than two prior systemic regimens for unresectable Stage III or Stage IV disease. All participants 12. Prior exposure to E7050 or lenvatinib. 13. Melanoma of intraocular origin. 14. participants who have received any anticancer treatment within 21 days (6 weeks for nitrosureas Cohort 1) or any investigational agent within 30 days prior to the first dose of study drug or who have not recovered from any acute toxicity related to previous anticancer treatment. 15. Major surgery within 3 weeks prior to the first dose of study drug. 16. Participants having greater than 1+ proteinuria on urinalysis will undergo 24-hour urine collection for quantitative assessment of proteinuria. Participants with urine protein greater than or equal to 1 g/24-hour will be ineligible. 17. Inability to take oral medication, gastrointestinal malabsorption, gastrointestinal anastomosis, or any other condition that might affect the absorption of E7050 or lenvatinib. 18. Significant cardiovascular impairment: history of congestive heart failure greater than New York Heart Association (NYHA) Class II, unstable angina, myocardial infarction or stroke within 6 months of the first dose of study drug; or cardiac arrhythmia requiring medical treatment. 19. Prolongation of QTc interval to greater than 480 msec. 20. Bleeding disorder or thrombotic disorder requiring anticoagulant therapy, such as warfarin, or similar agents requiring therapeutic INR monitoring (treatment with low molecular weight heparin \[LMWH\] is allowed). 21. Active hemoptysis (bright red blood of at least 0.5 teaspoon) within 3 weeks prior to the first dose of study drug. 22. Active infection (any infection requiring antibiotics). 23. Known intolerance or known hypersensitivity to any of the study drugs (or any of the excipients). 24. Any medical or other condition which, in the opinion of the investigator, would preclude participation in a clinical trial. 25. Females who are pregnant or breastfeeding.