Inclusion Criteria:  Histologically confirmed diagnosis of HCC. Have a tumor, not eligible for resection or local ablation. Have experienced disease progression under previous ≥ 4 cycles/12 weeks atezolizumab and bevacizumab therapy. Have a Child-Pugh Classification score ≤ 6 for assessed liver function within 7 days before allocation (Appendix 4) Have at least one measurable site of disease based on RECIST 1.1 with spiral CT scan or MRI. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions.  Male/female* participants who are at least 18 years of age on the day of signing informed consent will be enrolled in this study.  *There are no data that indicate special gender distribution. Therefore, patients will be enrolled in the study gender-independently.  A female participant is eligible to participate if she is not pregnant (see Appendix 3), not breastfeeding, and at least one of the following conditions applies:  Not a woman of childbearing potential (WOCBP) as defined in Appendix 3 OR A WOCBP who agrees to follow the contraceptive guidance in Appendix 3 during the treatment period and for at least 120 days after the last dose of study treatment.  A male participant with female partner of childbearing potential is eligible to participate if he agrees to follow the contraceptive guidance in Appendix 3 during the treatment period and for at least 120 days after the last dose of study treatment.  A male participant must agree to use a contraception as detailed in Appendix 3 of this protocol during the treatment period and for at least 210 days after the last dose of study treatment and refrain from donating sperm during this period. The participant provides written informed consent for the trial.  Either pre-treatment tumor tissue available  Newly obtained biopsies are preferred to archived tissue (archived specimen ≤ 6 months may be acceptable). Core or excisional biopsies mandatory (fine needle aspiration and bone metastasis samples are not acceptable). Formalin-fixed, paraffin embedded (FFPE) tissue blocks are preferred to slides. If submitting 15 unstained cut slides, newly cut slides should be submitted to the IKF GmbH lab within 14 days from the date slides are cut.  OR tumor tissue is not available as e.g., patient has never undergone biopsy or tissue depleted because of prior diagnostic testing  Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1. Evaluation of ECOG is to be performed within 7 days prior to the date of allocation. Have a life expectancy of ≥ 12 weeks.  Have adequate organ function as defined in the following table (Table 2). Specimens must be collected within 7 days prior to the start of study intervention.  Table 2: Adequate Organ Function Laboratory Values System Laboratory Value Hematological Absolute neutrophil count (ANC) ≥ 1500/µL Platelets ≥ 75000/µL Hemoglobin ≥ 8.0 g/dLa Renal Creatinine OR Measured or calculatedb creatinine clearance (GFR can also be used in place of creatinine or CrCl) ≤ 1.5 × ULN OR  ≥ 40 mL/min for participant with creatinine levels > 1.5 × institutional ULN Hepatic Total bilirubin ≤ 2 mg/dL OR direct bilirubin ≤ ULN for participants with total bilirubin levels > 2 mg/dL AST (SGOT) and ALT (SGPT) ≤ 5 × ULN Albumin ≥ 3.0 g/dL Pancreatic Amylase ≤ 1.5 × ULN Lipase ≤ 1.5 × ULN Coagulation International normalized ratio (INR) OR prothrombin time (PT) Activated partial thromboplastin time (aPTT) ≤ 1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants ALT (SGPT)=alanine aminotransferase (serum glutamic pyruvic transaminase); AST (SGOT)=aspartate aminotransferase (serum glutamic oxaloacetic transaminase); GFR=glomerular filtration rate; ULN=upper limit of normal.  a Transfusion are permitted to meet criteria. b Creatinine clearance (CrCl) should be calculated per institutional standard. Note: This table includes eligibility-defining laboratory value requirements for treatment; laboratory value requirements should be adapted according to local regulations and guidelines for the administration of specific chemotherapies.  Participants with past or ongoing HCV infection will be eligible for the study. The treated participants must have completed their treatment at least 1 month prior to starting study intervention and HCV viral load must be below the limit of quantification.  Participants with controlled hepatitis B will be eligible if they meet the following criteria:  Antiviral therapy for HBV must be given for at least 4 weeks and HBV viral load must be less than 500 IU/mL prior to first dose of study drug. Participants on active HBV therapy with viral loads under 100 IU/mL should stay on the same therapy throughout study intervention. Participants who are positive for anti-hepatitis B core antibody HBc, negative for HBsAg, and negative or positive for anti-hepatitis B surface antibody (HBs), and who have an HBV viral load under 100 IU/mL, do not require HBV antiviral prophylaxis. Has adequately controlled blood pressure with or without antihypertensive medications, defined as BP ≤ 150/90 mm Hg at Screening and no change in antihypertensive medications within 1 week before Cycle 1 Day 1.  Exclusion Criteria:  Known fibrolamellar HCC, sarcomatoid HCC, or mixed cholangiocarcinoma and HCC. Have received prior therapy with any TKI and/ or anti-PD-1, anti-PD-L1, or anti PD L2 agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g., CTLA-4, OX 40, CD137) other than atezolizumab and bevacizumab.  A WOCBP who has a positive urine pregnancy test within 72 hours prior to allocation (see Appendix 3). If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required.  Note: in the event that 24 hours have elapsed between the screening pregnancy test and the first dose of study treatment, another pregnancy test (urine or serum) must be performed and must be negative in order for subject to start receiving study medication.  Have received prior systemic anti-cancer therapy including investigational agents within 4 weeks or at least 5 half-lives of the respective drug/IMP (whichever is longer) prior to allocation.  Note: Participants must have recovered from all AEs due to previous therapies to ≤ Grade 1 or baseline. Participants with ≤ Grade 2 neuropathy may be eligible.  Note: If participant received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study intervention.  Have received prior radiotherapy within 2 weeks of start of study intervention. Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (≤ 2 weeks of radiotherapy) to non-CNS disease. Have received a live vaccine or live-attenuated vaccine within 30 days prior to the first dose of study drug. Administration of killed vaccines is allowed.  Are currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks or for a period of at least 5 half-lives of the respective drug/IMP (whichever is longer) before Screening and during Screening for this trial.  Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks or at least 5 half-lives of the respective drug/IMP (whichever is longer) after the last dose of the previous investigational agent.  Have a diagnosis of immunodeficiency or are receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug.  Have a known additional malignancy that is progressing or has required active treatment within the past 2 years.  Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin or carcinoma in situ (e.g., breast carcinoma, cervical cancer in situ) that have undergone potentially curative therapy are not excluded.  Have known active CNS metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e., without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at least 14 days prior to first dose of study treatment. Have severe hypersensitivity (≥ Grade 3) to lenvatinib, pembrolizumab and/or any of its excipients. Have a history of congestive heart failure NYHA > Class II, unstable angina, myocardial infarction or stroke within 6 months of the first dose of study treatment, or cardiac arrhythmia requiring medical treatment at Screening  Have bleeding or thrombotic disorders or subjects at risk for severe hemorrhage.  Note: 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.  Have active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment and is allowed. Have a history of (non-infectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease. Have an active infection requiring systemic therapy (exception: HBV infection - see inclusion criteria). Have a history of Human Immunodeficiency Virus (HIV) (mandatory testing for HIV during screening is required). Have a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the participant's participation for the full duration of the study, or is not in the best interest of the participant to participate, in the opinion of the treating Investigator. Have known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. Are pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of study treatment. Are unable to swallow orally administered medication or have gastrointestinal disorders likely to interfere with absorption of the study medication. Legal incapacity or limited legal capacity.