Trial to Assess Safety and Efficacy of Lenvatinib (18 mg vs. 14 mg) in Combination With Everolimus in Participants With Renal Cell Carcinoma

Inclusion Criteria:

* Histological or cytological confirmation of predominant clear cell renal cell carcinoma (RCC) (original tissue diagnosis of RCC is acceptable)
* Documented evidence of advanced RCC
* One prior disease progression episode on or after vascular endothelial growth factor (VEGF)-targeted treatment (for example, but not limited to, sunitinib, sorafenib, pazopanib, cabozantinib, bevacizumab, axitinib, vatalanib, AV951/tivozanib) administered for the treatment of RCC. Prior programmed cell death protein 1 (PD-1)/programmed death-ligand 1 (PD-L1) treatment in addition to 1 prior VEGF-targeted treatment is allowed.
* At least 1 measurable target lesion according to Response Evaluation Criteria in Solid Tumors (RECIST 1.1) meeting the following criteria:

  * Lymph node (LN) lesion that measures at least 1 dimension as \>=1.5 centimeter (cm) in the short axis;
  * Non-nodal lesion that measures \>=1.0 cm in the longest diameter;
  * The lesion is suitable for repeat measurement using computerized tomography/magnetic resonance imaging (CT/MRI). Lesions that have had external beam radiotherapy (EBRT) or locoregional therapy must show radiographic evidence of disease progression based on RECIST 1.1 to be deemed a target lesion.
* Male or female participants age \>=18 years (or any age \>=18 years if that age is considered to be an adult per the local jurisdiction) at the time of informed consent
* Karnofsky Performance Status (KPS) of \>=70
* Adequately controlled blood pressure (BP) with or without antihypertensive medications, defined as BP less than or equal to (\<=) 150/90 millimeters of mercury (mmHg) at Screening and no change in antihypertensive medications within 1 week before Cycle 1/Day 1
* Adequate renal function defined as calculated creatinine clearance \>=30 milliliters per minute (mL/min) per the Cockcroft and Gault formula
* Adequate bone marrow function defined by:

  * Absolute neutrophil count (ANC) \>=1500/millimeters cubed (mm\^3) (\>=1.5\*10\^9/Liters \[L\]);
  * Platelets \>=100,000/mm\^3 (\>=100\*10\^9/L);
  * Hemoglobin \>=9 grams per deciliter (g/dL)
* Adequate blood coagulation function defined by International Normalized Ratio (INR) \<=1.5 (except for participants on warfarin therapy where INR must be \<=3.0 prior to randomization)
* Adequate liver function defined by:

  * Total bilirubin \<=1.5 times the upper limit of normal (ULN) except for unconjugated hyperbilirubinemia of Gilbert's syndrome;
  * Alkaline phosphatase (ALP), alanine aminotransferase (ALT), and aspartate aminotransferase (AST) \<=3\* the ULN (in the case of liver metastases \<=5\* the ULN). Participants with bone metastases with ALP values greater than 3 times can be included.
* Participant must voluntarily agree to provide written informed consent
* Participant must be willing and able to comply with all aspects of the protocol

Exclusion Criteria:

* More than 1 prior VEGF-targeted treatment for advanced RCC
* Participants with Central Nervous System (CNS) metastases are not eligible, unless they have completed local therapy for at least 4 weeks and have discontinued the use of corticosteroids for this indication or are on a tapering regimen of corticosteroids (defined as \<=10 mg prednisolone equivalent) before starting treatment in this study. Any signs (example, radiologic) or symptoms of brain metastases must be stable for at least 4 weeks before starting study treatment.
* Active malignancy (except for RCC or definitively treated basal or squamous cell carcinoma of the skin, or carcinoma in-situ of the cervix or bladder) within the past 24 months
* Any anti-cancer treatment (except for radiation therapy) within 21 days, or any investigational agent within 30 days prior to the first dose of study drug; participants should have recovered from any toxicity related to previous anti-cancer treatment to Common Toxicity Criteria (CTC) grade 0 or 1.
* Prior radiation therapy within 21 days prior to the start of study treatment with the exception of palliative radiotherapy to bone lesions, which is allowed if completed 2 weeks prior to study treatment start
* Known intolerance to study drug (or any of the excipients) and/or known hypersensitivity to rapamycins (example, sirolimus, everolimus, temsirolimus) or any of the excipients
* Participants with proteinuria greater than (\>) 1+ on urinalysis will undergo 24-hour urine collection for quantitative assessment of proteinuria. Participants with urine protein \>=1 g/24 hour will be ineligible.
* Fasting total cholesterol ˃300 mg/dL (or ˃7.75 millimoles \[mmol\]/L) and/or fasting triglycerides level ˃2.5\* the ULN. Note: these participants can be included after initiation or adjustment of lipid-lowering medication.
* Uncontrolled diabetes as defined by fasting glucose \>1.5 times the ULN. Note: these participants can be included after initiation or adjustment of glucose-lowering medication.
* Prolongation of QT corrected (QTc) interval to \>480 milliseconds (ms)
* Participants who have not recovered adequately from any toxicity and/or complications from major surgery prior to starting therapy
* Gastrointestinal malabsorption, gastrointestinal anastomosis, or any other condition that might affect the absorption of lenvatinib or everolimus
* Bleeding or thrombotic disorders or participants at risk for severe hemorrhage. The degree of tumor invasion/infiltration of major blood vessels (example, carotid artery) should be considered because of the potential risk of severe hemorrhage associated with tumor shrinkage/necrosis following lenvatinib therapy.
* Clinically significant hemoptysis or tumor bleeding within 2 weeks prior to the first dose of study drug
* Significant cardiovascular impairment within 6 months prior to the first dose of study drug; history of congestive heart failure greater than New York Heart Association (NYHA) Class II, unstable angina, myocardial infarction or stroke, or cardiac arrhythmia associated with significant cardiovascular impairment or left ventricular ejection fraction (LVEF) below the institutional normal range as determined by screening multigated acquisition (MUGA) scan or echocardiogram.
* Active infection (any infection requiring systemic treatment)
* Any medical or other condition that in the opinion of the investigator(s) would preclude the participant's participation in a clinical study
* Females who are breastfeeding or pregnant at Screening or Baseline (as documented by a positive beta-human chorionic gonadotropin \[β-hCG\] (or human chorionic gonadotropin \[hCG\]) test with a minimum sensitivity of 25 International Units per Liter \[IU/L\] or equivalent units of β-hCG \[or hCG\]). A separate baseline assessment is required if a negative screening pregnancy test was obtained more than 72 hours before the first dose of study drug.
* Females of childbearing potential who (Note: all females will be considered to be of childbearing potential unless they are postmenopausal \[amenorrheic for at least 12 consecutive months, in the appropriate age group, and without other known or suspected cause\] or have been sterilized surgically \[that is, bilateral tubal ligation, total hysterectomy, or bilateral oophorectomy, all with surgery at least 1 month before dosing\].):

  * do not agree to use a highly effective method of contraception for the entire study period and for up to 8 weeks after study drug discontinuation, that is:

    * total abstinence (if it is their preferred and usual lifestyle)
    * an intrauterine device (IUD) or hormone releasing system (IUS)
    * a contraceptive implant
    * an oral contraceptive (with additional barrier method) (Note: Participants must be on a stable dose of the same oral hormonal contraceptive product for at least 4 weeks before dosing with study drug and for the duration of the study.) OR
  * do not have a vasectomized partner with confirmed azoospermia

For sites outside of the European Union, it is permissible that if a highly effective method of contraception is not appropriate or acceptable to the participant, then the participant must agree to use a medically acceptable method of contraception, that is, double barrier methods of contraception, such as condom plus diaphragm or cervical/vault cap with spermicide.