The goal of this clinical trial is to learn if lenvatinib or regorafenib can help treat people with advanced liver cancer (hepatocellular carcinoma, HCC) that cannot be removed with surgery after first treatment with immunotherapy-based drug combinations. It will also look at the safety of these treatments. The main questions this study aims to answer are: * How long lenvatinib can delay cancer growth in people with good liver function (Child-Pugh)A after dual immunotherapy * How long people with reduced liver function (Child-Pugh B7-B8) live after treatment with lenvatinib or regorafenib after first-line immunotherapy-based combination treatment * What side effects people experience during treatment * How many people have their tumors shrink or disappear The study has two parts: In REVIVE-1, participants with Child-Pugh A liver function will receive lenvatinib. In REVIVE-2, participants with Child-Pugh B7 to B8 liver function will receive either lenvatinib or regorafenib. Participants will: * take lenvatinib or regorafenib by mouth * visit the clinic regularly for physical exams, blood and urine tests, and safety checks * have computed tomography (CT) scans every 8 weeks to check their cancer * be followed during and after treatment to assess outcomes and side effects
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Progression-Free Survival (PFS) in REVIVE-1
Timeframe: Up to 24 months
Overall Survival (OS) in REVIVE-2
Timeframe: Up to 30 months