Inclusion Criteria:  Adults (≥18 years old) with histologically or cytologically confirmed HCC beyond Milan Criteria Must be treatment naïve and eligible for TACE procedure Must be on the liver transplant waiting list and not require any other solid organ transplant Eastern Cooperative Oncology Group performance status of 0 or 1 Patients with hepatitis B virus (HBV) infection (as characterized by positive HBV surface antigen and/or anti-hepatitis B core antibodies (HBcAbs) with detectable HBV DNA (≥10 IU/mL or above the limit of detection per local laboratory) must receive antiviral therapy at least after study enrollment per institutional practice to ensure adequate viral suppression (HBV DNA ≤2000 IU/mL). Patients must be managed for 6 months after the last dose of study treatment. Antiviral therapy will be concurrent with lenvatinib. Patients with hepatitis C virus (HCV) infection (as characterized by the presence of detectable HCV RNA or anti-HCV antibody) must be managed per local institutional practice and for 6 months after the last dose of study treatment. Antiviral therapy will be concurrent with lenvatinib. For females of reproductive potential: use of highly effective contraception for at least 1 month prior to screening and agreement to use such a method during study participation For males of reproductive potential: use of condoms or other methods to ensure effective contraception with partner while undergoing active treatment up to 1 week after  Adequate organ and marrow function, as defined below:  Hemoglobin ≥9 g/dL Platelet count ≥50,000/μL Total bilirubin ≤3.0 Albumin ≥2 g/dL International normalized ratio ≤2 Cardiac ejection fraction ≥45% Able to swallow orally administered medication Capable of signing informed consent form (ICF) and complying with the study protocol, in the investigator's judgement  Exclusion Criteria:  Mixed hepatocellular-cholangiocarcinoma or HCC within Milan criteria Previously received chemotherapy or immunotherapy for HCC Child Pugh assessment score greater than or equal to B8 Uncontrolled blood pressure (BP; Systolic BP>140 mmHg or diastolic BP >90 mmHg) despite an optimized regimen of antihypertensive medication Electrolyte abnormalities that have not been corrected 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 at Screening Bleeding or thrombotic disorders or subjects at risk for severe hemorrhage. The degree of tumor invasion/infiltration of major blood vessels (e.g. carotid artery) should be considered because of the potential risk of severe hemorrhage associated with tumor shrinkage/necrosis following lenvatinib therapy Participants having > 1+ proteinuria on urine dipstick testing unless a 24-hour urine collection for quantitative assessment indicates that the urine protein is <1 g/24 hours Evidence of portal vein thrombosis that precludes the TACE procedure  History of another primary malignancy except for the following:  Prostate cancer of pathologic stage less than or equal to T2cN0M0 determined from a prior prostatectomy without biochemical recurrence and who, in the opinion of the investigator, are not deemed to require active intervention, or patients with incidental histologic findings of prostate cancer that has not been treated prior to the study and who do not require specific therapy for prostate cancer beyond surgery and also are considered to be at low risk for recurrence per the investigator Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease Adequately treated carcinoma in situ without evidence of disease Active infection, including tuberculosis or human immunodeficiency virus Known intolerance to lenvatinib or any of the excipients Females who are breastfeeding or pregnant Females of childbearing potential who do not agree to use highly effective contraception during the active treatment phase of the study and for 30 days after the last dose of the study treatment Males who do not agree to use highly effective contraception during the active treatment phase of the study and for 30 days after the last dose of the study treatment