This is a multicenter, open-label, non-randomized Phase 1 study in participants with advanced solid tumors, excluding hepatocellular carcinoma (HCC), that have progressed after treatment with approved therapies, or for which there are no standard therapies available. The study will also include participants with radioiodine-refractory differentiated thyroid cancer (RR-DTC). Its primary intent is to determine the effect of lenvatinib on CYP3A4 activity as well as to assess the safety and activity of lenvatinib in these participants. The study will be conducted in the following 3 phases: Pretreatment Phase, Treatment Phase, and Extension Phase.

Inclusion Criteria:

1. Age greater than or equal to 18 years at the time of informed consent.

2. Histologically or cytologically confirmed advanced solid tumors (excluding HCC) that have progressed following standard therapy, or for which no standard therapy exists (including surgery or radiation therapy) or participants with RR-DTC.

3. Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1.

4. Life expectancy greater than or equal to 3 months.

5. Adequately controlled blood pressure (BP) with or without antihypertensive medications, defined as BP less than or equal to 150/90 mmHg at screening and no change in antihypertensive medications within 1 week prior to the Cycle 1 Day 1.

6. Adequate renal function defined as calculated creatinine clearance greater than or equal to 30 mL/min per the Cockcroft and Gault formula.

7. Adequate bone marrow function:

   1. Absolute neutrophil count (ANC) greater than or equal to 750/mm3 (greater than or equal to 0.75 X 10^9/L)
   2. Platelets greater than or equal to 75,000/mm3 (greater than or equal to 75 X 10^9/L)
   3. Hemoglobin greater than or equal to 9.0 g/dL

8. Adequate blood coagulation function as evidenced by an International Normalized Ratio (INR) less than or equal to 1.5.

9. Adequate liver function:

   1. Total bilirubin less than or equal to 1.5 X the upper limit of normal (ULN) except for unconjugated hyperbilirubinemia of Gilbert's syndrome
   2. Alkaline phosphatase (ALP), alanine aminotransferase (ALT), and aspartate aminotransferase (AST) less than or equal to 3 X ULN (less than or equal to 5 X ULN if participant has liver metastases). If ALP is greater than 3 X ULN (in the absence of liver metastases) or greater than 5 X ULN (in the presence of liver metastases) AND the participant also is known to have bone metastases, the liver-specific ALP must be separated from the total and used to assess the liver function instead of total ALP.

10. Participants with Hepatitis B or C are eligible on the condition that they have adequate liver function as defined by Inclusion Criterion 9.

11. All prior therapy related toxicities must have resolved to Grade less than 2 severity per Common Terminology Criteria for Adverse Events (CTCAE version 4.03), except alopecia and infertility.

12. Left ventricular ejection fraction (LVEF) greater than 50% on echocardiography or multiple gated acquisition (MUGA) scan.

13. Females must not be lactating or pregnant at screening or baseline (as documented by a negative beta-human chorionic gonadotropin [B-hCG] test with a minimum sensitivity of 25 IU/L or equivalent units of B-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.

14. Participant must voluntarily agree to provide written informed consent.

15. Participant must be willing and able to comply with all aspects of the protocol.

Exclusion Criteria:

1. Participants with diagnosis of HCC.
2. Participants with anaplastic thyroid carcinoma with major blood vessel invasion or infiltration.
3. Participants having greater than (>) 1 plus (+) proteinuria on urine dipstick testing will undergo 24-hour urine collection for quantitative assessment of proteinuria. Participants with urine protein greater than or equal to (>=1) gram per 24 hours will be ineligible.
4. Participants with known leptomeningeal metastases or untreated brain metastases. Participants with known brain metastases will be eligible if they have completed the primary brain therapy (such as whole brain radiotherapy, stereotactic radiosurgery, or complete surgical resection) and if they have remained clinically stable, asymptomatic, and off steroids for at least 28 days.
5. Participants taking medications that are known potent CYP3A4 inducers/inhibitors or substrates with narrow therapeutic indices or St. John's Wort.
6. Participants unwilling to exclude grapefruit juice and grapefruit from their diet.
7. Participants who have received any anticancer treatment within 3 weeks or any investigational agent within 30 days before the first dose of study drug or who have not recovered from any acute toxicity greater than Grade 0 or 1 related to previous anticancer treatment.
8. Major surgery within 4 weeks before the first dose of study drug.
9. Inability to take oral medication, or malabsorption syndrome or any other uncontrolled gastrointestinal condition (eg, nausea, diarrhea, or vomiting) that might impair the bioavailability of lenvatinib or midazolam.
10. Significant cardiovascular impairment: history of congestive heart failure greater than New York Heart Association (NYHA) Class II, uncontrolled arterial hypertension, unstable angina, myocardial infarction, or stroke within 6 months of the first dose of study drug; or cardiac arrhythmia requiring medical treatment (including oral anticoagulation).
11. A clinically significant electrocardiogram (ECG) abnormality (ie, corrected QT interval [QTc] interval greater than 480 msec when electrolyte balance is normal), or a history of risk factors for torsade de pointes, hypokalemia, long QT syndrome, or the use of concomitant medications resulting in a prolongation of QTc interval.
12. Active hemoptysis (bright red blood of at least 2.5 mL ie, half teaspoon) within 3 weeks prior to the first dose of study drug.
13. Active infection (any infection requiring treatment).
14. Known hypersensitivity to any component of lenvatinib or midazolam.
15. Prior treatment with lenvatinib.
16. Achlorhydria or use of antacids, proton-pump inhibitors, or other drugs known to raise gastric pH within 2 weeks before study drug administration.
17. Immunocompromised participants, including participants known to be infected with human immunodeficiency virus (HIV).
18. Any other major illness that, in the investigator's judgment, will substantially increase the risk associated with the participant's participation in this study.
19. Participants who meet any of the following criteria will be excluded from this study:

Females who are breastfeeding or pregnant at Screening or Baseline (as documented by a positive beta-human chorionic gonadotropin [ß-hCG] (or human chorionic gonadotropin [hCG]) test with a minimum sensitivity of 25 international units per liter (IU/L) or equivalent units of ß-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.

OR Females of childbearing potential who do not agree to use a highly effective method of contraception for the entire study period and for 28 days after study drug discontinuation i.e. i) total abstinence (if it is their preferred and usual lifestyle) ii) an intrauterine device (IUD) or hormone releasing system (IUS) iii) a contraceptive implant iv. an oral contraceptive (with additional barrier method) OR who do not have a vasectomized partner with confirmed azoospermia. For sites outside of the European Union (EU), 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, i.e. double barrier methods of contraception such as condom plus diaphragm or cervical/vault cap with spermicide. 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]