A Trial to Evaluate Efficacy and Safety of Lenvatinib in Combination With Everolimus in Subjects With Unresectable Advanced or Metastatic Non Clear Cell Renal Cell Carcinoma (nccRCC) Who Have Not Received Any Chemotherapy for Advanced Disease

Inclusion Criteria: * Males or females age ≥18 years at the time of informed consent form (ICF) * Participants with histologically confirmed non clear cell renal cell carcinoma (nccRCC) who have not received any chemotherapy for advanced disease. Participants must have one of the following subtypes of nccRCC: papillary, chromophobe, collecting duct carcinoma (CDC), renal medullary carcinoma (RMC), or unclassified. * Radiologically measurable disease meeting the following criteria: 1. At least 1 lesion of ≥10 millimeters (mm) in the longest diameter for a nonlymph node or ≥15 mm in the short axis diameter for a lymph node that is serially measurable according to Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 using computerized tomography (CT) or magnetic resonance imaging (MRI); 2. Lesions that have had external beam radiotherapy (EBRT) or locoregional therapies such as radiofrequency (RF) ablation must show evidence of subsequent progressive disease (substantial size increase of ≥20%) to be deemed a target lesion. * Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1. * Blood pressure (BP) ≤140/90 millimeters of mercury (mmHg) at Screening with or without antihypertensive medications and no change in antihypertensive medications within 1 week prior to Cycle 1/Day 1. * Adequate renal function as evidenced by calculated creatinine clearance ≥30 milliliters (mL)/minute according to the Cockcroft and Gault formula * Adequate bone marrow function: 1. Absolute neutrophil count (ANC) ≥1.5 × 10\^9/liter (L); 2. Hemoglobin ≥10.0 grams per deciliter (g/dL) (can be corrected by growth factor or transfusion prior to first dose of study drug); 3. Platelet count ≥100 × 10\^9/L * Adequate liver function: 1. Bilirubin ≤1.5 × upper limit of normal (ULN) except for unconjugated hyperbilirubinemia or Gilbert's syndrome; 2. Alkaline phosphatase (ALP), alanine aminotransferase (ALT), and aspartate aminotransferase (AST) ≤3 × ULN (≤5 × ULN if participant has liver metastases). If ALP is \>3 × ULN (in the absence of liver metastases) or \>5 × ULN (in the presence of liver metastases) AND participants are also known to have bone metastases, the liver-specific ALP must be separated from the total and used to assess the liver function instead of the total ALP. * Voluntary agreement to provide written informed consent and the willingness and ability to comply with all aspects of the protocol Exclusion Criteria: * Predominant clear cell renal cell carcinoma (RCC) * Prior anticancer chemotherapy or targeted therapy for advanced nccRCC * Prior exposure to lenvatinib or mammalian target of rapamycin (mTOR) inhibitor * Known intolerance to lenvatinib, everolimus (or other rapamycin derivatives), or any of the excipients * Major surgery performed within 3 weeks prior to the first dose of study drugs or scheduled for major surgery during the study * Gastrointestinal malabsorption, gastrointestinal anastomosis, or any other condition that might affect the absorption of lenvatinib or everolimus * Participants having \>1+ proteinuria on urine dipstick testing will undergo 24 hour urine collection for quantitative assessment of proteinuria. Participants with urine protein ≥1 grams (g)/24 hours will be ineligible. * Fasting total cholesterol ˃300 milligrams (mg)/dL (or ˃7.75 millimoles \[mmol\]/L) or fasting triglycerides level ˃2.5 × 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: In case this threshold is exceeded, these participants can only be included after initiation or adjustment of glucose-lowering medication. * Known history of, or any evidence of, interstitial lung disease or active noninfectious pneumonitis. * 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 * Prolongation of QTcF interval to \>480 milliseconds (msec) * Known history of human immunodeficiency virus (HIV) positive * Known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] RNA detected) * Clinically significant hemoptysis or tumor bleeding within 2 weeks prior to the first dose of study drug * Participants with central nervous system (CNS) (e.g., brain or leptomeningeal) metastases. * Other active malignancy (except definitively treated melanoma in-situ, basal or squamous cell carcinoma of the skin, or carcinoma in-situ of the cervix or bladder) within the past 24 months * 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 \[IU\]/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: 1. Had unprotected sexual intercourse within 30 days before study entry and who do not agree to use a highly effective method of contraception (e.g., total abstinence, an intrauterine device, a double-barrier method \[such as a condom plus diaphragm with spermicide\], a contraceptive implant, an oral contraceptive, or have a vasectomized partner with confirmed azoospermia) throughout the entire study period and for 28 days after study drug discontinuation 2. Are currently abstinent, and do not agree to use a double-barrier method (as described above) or refrain from being sexually active during the study period or for 28 days after study drug discontinuation 3. Are using hormonal contraceptives but are not on a stable dose of the same hormonal contraceptive product for at least 4 weeks before dosing and who do not agree to use the same contraceptive during the study or for 28 days after study drug discontinuation 4. Are using oral hormonal contraceptives and who do not agree to add a barrier method • 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 (i.e., bilateral tubal ligation, total hysterectomy, or bilateral oophorectomy, all with surgery at least 1 month before dosing). * Males who have not had a successful vasectomy (confirmed azoospermia) or they and their female partners do not meet the criteria above (i.e., not of childbearing potential or practicing highly effective contraception throughout the study period or for 28 days after study drug discontinuation). No sperm donation is allowed during the study period and for 28 days after study drug discontinuation. * Evidence of clinically significant disease (e.g., cardiovascular, respiratory, gastrointestinal, renal, or infectious disease) that in the opinion of the investigator(s) could affect the participant's safety or interfere with the study assessments * Any medical or other condition that in the opinion of the investigator(s) would preclude the participant's participation in a clinical study * Active and current use of illegal recreational drugs * Currently enrolled in another interventional clinical study or used any investigational drug or device within the past 28 days preceding informed consent