• Number of Participants with Dose-limiting Toxicities (DLTs) [ Time Frame: Cycle 0 (Cycle length is 6 or 7 days) up to Cycle 1 (Cycle length is 28 days) ]
  DLT will be defined as any of the events that are considered by the investigator to be at least possibly related to therapy with the study medication. Toxicity will be evaluated according to National Cancer Institute Common Terminology Criteria for Adverse Events version 5.0 (NCI CTCAE 5.0).
• Number of Participants with Adverse Events (AEs) and Serious Adverse Events (SAEs) [ Time Frame: Up to 30 days after the last dose of study drug or before initiating post anti-cancer treatment (approximately 2 years) ]

• Cmax: Maximum Observed Plasma Concentration for E7386 [ Time Frame: Cycle 0 Day 1: 0-24 hours; Cycle 0 Day 5 or Day 6: 0-48 hours (Cycle length is 6 or 7 days); Cycle 1 Day 8: 0-24 hours (Cycle length is 28 days) ]
• Tmax: Time to Reach the Maximum Plasma Concentration (Cmax) for E7386 [ Time Frame: Cycle 0 Day 1: 0-24 hours; Cycle 0 Day 5 or Day 6: 0-48 hours (Cycle length is 6 or 7 days); Cycle 1 Day 8: 0-24 hours (Cycle length is 28 days) ]
• AUC: Area Under the Plasma Concentration Versus Time Curve for E7386 [ Time Frame: Cycle 0 Day 1: 0-24 hours; Cycle 0 Day 5 or Day 6: 0-48 hours (Cycle length is 6 or 7 days); Cycle 1 Day 8: 0-24 hours (Cycle length is 28 days) ]
• CL/F: Apparent Total Body Clearance for E7386 [ Time Frame: Cycle 0 Day 1: 0-24 hours; Cycle 0 Day 5 or Day 6: 0-48 hours (Cycle length is 6 or 7 days); Cycle 1 Day 8: 0-24 hours (Cycle length is 28 days) ]
• Vz/F: Apparent Volume of Distribution for E7386 [ Time Frame: Cycle 0 Day 1: 0-24 hours; Cycle 0 Day 5 or Day 6: 0-48 hours (Cycle length is 6 or 7 days); Cycle 1 Day 8: 0-24 hours (Cycle length is 28 days) ]
• Percentage of Participants with Best Overall Response (BOR) [ Time Frame: From first dose of study drug until PD, development of unacceptable toxicity, participant requests to discontinue, withdrawal of consent or study termination (up to approximately 2 years) ]
  BOR is defined as complete response (CR), partial response (PR), stable disease (SD), PD, and not evaluable (NE), where SD has to be achieved at >= 7 weeks after the first dose. The BOR will be assessed by investigator based on Modified Response Evaluation Criteria in Solid Tumors (mRECIST) for HCC part or on Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 for ST-part.
• Objective Response Rate (ORR) [ Time Frame: From first dose of study drug until PD, development of unacceptable toxicity, participant requests to discontinue, withdrawal of consent or study termination (up to approximately 2 years) ]
  The ORR is defined as the percentage of participants with a BOR of CR or PR. The ORR will be assessed by investigator based on mRECIST for HCC part or on RECISTversion 1.1 for ST-part.
• Disease Control Rate (DCR) [ Time Frame: From first dose of study drug until PD, development of unacceptable toxicity, participant requests to discontinue, withdrawal of consent or study termination (up to approximately 2 years) ]
  DCR is defined as the percentage of participants with a BOR of CR, PR, or SD. The DCR will be assessed by investigator based on mRECIST for HCC part or on RECISTversion 1.1 for ST-part.
• Clinical Benefit Rate (CBR) [ Time Frame: From first dose of study drug until PD, development of unacceptable toxicity, participant requests to discontinue, withdrawal of consent or study termination (up to approximately 2 years) ]
  The CBR is defined as the percentage of participants with a BOR of CR, PR, or durable SD (duration of SD >=23 weeks). The CBR will be assessed by investigator based on mRECIST for HCC part or on RECISTversion 1.1 for ST-part.
• Progression-free Survival (PFS) [ Time Frame: From first dose of study drug until PD, or death from any cause, whichever occurs first (up to approximately 2 years) ]
  PFS is defined as the time from the date of the first dose to the date of the first documentation of confirmed PD or death, whichever occurs first.

• Neoplasms
• Carcinoma, Hepatocellular
• Liver Neoplasms

• Drug: E7386
  E7386, tablets, orally.
• Drug: Lenvatinib
  Lenvatinib, capsules, orally.
  Other Name: Lenvima

• Experimental: Hepatocellular Carcinoma (HCC) Part
  Participants with HCC will receive E7386 tablets, alone orally, once daily (QD) for 5 or 6 consecutive days followed by 48 hours of without treatment in Cycle 0 (6 or 7 days). Participants with HCC will receive E7386 tablets, orally, QD in combination with lenvatinib capsules, orally, QD in 28-day treatment cycles until disease progression (PD), development of unacceptable toxicity, participant's request to discontinue, withdrawal of consent, or termination of the study program. Dose escalation of E7386 will be based on the available safety data from the previous cohorts.
  Interventions:

  • Drug: E7386
  • Drug: Lenvatinib
• Experimental: Other Solid Tumor (ST) Part
  Participants with ST (except for HCC) will receive E7386 tablets, alone orally, QD for 5 or 6 consecutive days followed by 48 hours of without treatment in Cycle 0 (6 or 7 days). Participants with ST (except for HCC) will receive E7386 tablets, orally, QD in combination with lenvatinib capsules, orally in 28-day treatment cycles until PD, development of unacceptable toxicity, participant's request to discontinue, withdrawal of consent, or termination of the study program. Dose escalation of E7386 and lenvatinib will be based on the available safety data from the previous cohorts.
  Interventions:

  • Drug: E7386
  • Drug: Lenvatinib

Inclusion Criteria:

1. HCC part only:

   Participants with confirmed diagnosis of unresectable HCC with any of the following criteria:

   1. Histologically or cytologically confirmed diagnosis of HCC, excluding fibrolamellar, sarcomatoid or mixed cholangio-HCC tumors
   2. Clinically confirmed diagnosis of HCC according to American Association for the Study of Liver Diseases (AASLD) criteria, including cirrhosis of any etiology and/or chronic hepatitis B or C infection

   ST part only (except for HCC ):

   Participants with histologically or cytologically confirmed diagnosis of solid tumor for which no alternative standard therapy or no effective therapy exists

2. Life expectancy of >=12 weeks
3. Eastern Cooperative Oncology Group (ECOG) Performance Status of 0-1
4. All AEs due to previous anti-cancer therapy have either returned to Grade 0-1 except for alopecia (renal/bone marrow/liver function should meet the inclusion criteria).
5. Adequate controlled blood pressure (BP), renal function, bone marrow function, liver function, and serum mineral level
6. At least one measurable lesion based on mRECIST (HCC part) or on RECIST 1.1 (ST-part)
7. HCC part only: Child-Pugh score A
8. HCC part only: Participants categorized to stage B (not applicable for trans arterial chemoembolization), or stage C based on Barcelona Clinic Liver Cancer (BCLC) staging system

Exclusion Criteria:

1. Any of cardiac conditions as follows:

   1. Heart failure New York Heart Association (NYHA) Class II or above
   2. Unstable ischaemic heart disease (myocardial infarction within 6 months prior to starting study drug, or angina requiring use of nitrates more than once weekly)
   3. Prolongation of corrected QT (QTcF) interval to greater than (>) 480 millisecond (msec)
   4. Left ventricular ejection fraction (LVEF) <50 percent (%)
2. Known to be human immunodeficiency virus (HIV) positive
3. Participants with proteinuria >1+ on urine dipstick testing will undergo 24-h urine collection for quantitative assessment of proteinuria. Participants with urine protein >=1 gram per (g/) 24 hour will be ineligible
4. Diagnosed with meningeal carcinomatosis
5. Participants with brain or subdural metastases are not eligible, unless they have completed local therapy and have discontinued the use of corticosteroids for this indication for at least 4 weeks before starting treatment in this study Any signs (e.g., radiologic) or symptoms of brain metastases must be stable for at least 4 weeks before starting study treatment
6. Pulmonary lymphangitic involvement that results in pulmonary dysfunction requiring active treatment, including the use of oxygen
7. Bleeding or thrombotic disorders or use of anticoagulants requiring therapeutic International Normalized Ratio (INR) monitoring (e.g. warfarin or similar agents)
8. Gastrointestinal bleeding event or active hemoptysis (bright red blood of at least 0.5 teaspoon) within 3 weeks prior to the first dose of study drug