Inclusion Criteria:  Have a diagnosis of Hepatocellular Carcinoma (HCC) confirmed by radiology, histology, or cytology (fibrolamellar and mixed hepatocellular/cholangiocarcinoma subtypes are not eligible). Radiological confirmation of diagnosis is provided by the study site and defined by the presence of a liver mass of at least 1 cm and exhibiting arterial hypervascularity with washout in the portal venous phase seen in a tri-phasic magnetic resonance imaging (MRI). At least one measurable disease based on RECIST 1.1.  Low risk of surgical morbidity and mortality from liver surgery as defined by the following criteria:  Single tumour No requirement for vascular resection Expected residual liver volume 40% Minor (up to 3 segments) or major resection (up to 5 segments)  If non-cirrhotic based on history, imaging, liver function +/- uninvolved liver biopsy):  • Single tumour any size  If cirrhotic  Single tumour ≤ 5cm  Major resection (up to 5 segments) only with good liver function as defined locally by:  Normal Bilirubin and No varices on pre-operative computerised tomography (CT) Wedge pressure < 10mmHg or Biopsy of uninvolved liver showing mild cirrhosis (Ashak grading) Child-Pugh A liver disease International normalised ratio (INR) ≤1.4 ECOG Performance status 0 or 1  Adequate haematological function as defined by:  Haemoglobin (Hb) > 90g/l Neutrophil Count > 1.5 x 109/l Platelets > 75 x 109/l Adequate renal function with GFR >40ml/min using a validated creatinine clearance calculation (e.g. Cockcroft-Gault or Wright formula)  Adequate liver function as defined by:  Aminotransferase (ALT) or aspartate aminotransferase (AST) < 5.0 x ULN Albumin >32g/l Amylase and lipase ≤ 1.5 x ULN Patients with past or ongoing hepatitis C virus (HCV) infection will be eligible for the study. The treated patients must have completed their treatment at least 1 month prior to starting  Patients with controlled hepatitis B will be eligible as long as they meet the following criteria:  Antiviral therapy for hepatitis B virus (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. Patients on active HBV therapy with viral loads under 500 IU/mL should stay on the same therapy throughout study treatment. Patients who are positive for anti-hepatitis B core antibody (HBc), negative for hepatitis B surface antigen (HBsAg), and negative or positive for anti-hepatitis B surface antibody (HBs), and who have an HBV viral load under 500 IU/mL, do not require HBV anti-viral prophylaxis 18 years of age or over Predicted life expectancy of > 3 months Patients must have given written informed consent Patients must have the ability to swallow oral medication  Exclusion Criteria:  Has received any systemic chemotherapy, including anti-VEGF therapy, or any systemic investigational anticancer agents for advanced/unresectable HCC. Has received local therapy including trans arterial embolic, chemo- or radiotherapy, external beam radiotherapy or ablative therapy to the measurable lesion to be resected. Has received prior therapy with an 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, or CD137). Oesophageal or gastric variceal bleeding within the last 6 months. Has received a live vaccine within 30 days prior to registration (seasonal flu vaccines that do not contain live virus are permitted). Administration of killed vaccines is allowed.  Active autoimmune disease that has required systemic treatment (i.e., with use of disease-modifying agents, corticosteroids or immunosuppressive drugs) in past 2 years except  Vitiligo Psoriasis Autoimmune-related hyperthyroidism Autoimmune-related hypothyroidism who are in remission or on a stable dose of thyroid-replacement hormone replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed. Has a history of (non-infectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease. A diagnosis of immunodeficiency or is receiving systemic steroid therapy (>10mg daily prednisolone equivalent) or any other form of immunosuppressive therapy within 7 days prior to treatment. Has a known additional malignancy that is progressing or has required active treatment within the past 3 years. Note: Patients 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. Has clinically apparent ascites on physical examination that is not controlled with medication. Note: ascites detectable on imaging studies only are allowed. Uncontrolled blood pressure (Systolic BP)>150 mmHg or diastolic BP >90 mmHg) in spite of an optimised regimen of anti-hypertensive medication. Has had clinically diagnosed hepatic encephalopathy in the last 6 months. Patients on rifaximin or lactulose to control their hepatic encephalopathy are not allowed. Has medical contraindications that preclude all forms of contrast enhanced imaging (tri-phasic CT or MRI). Gastrointestinal malabsorption, gastrointestinal anastomosis, or any other condition that might affect the absorption of lenvatinib. Has a pre-existing Grade ≥3 gastrointestinal or non-gastrointestinal fistula. Clinically significant haemoptysis from any source or tumour bleeding within 2 weeks prior to start of treatment. Electrolyte abnormalities that have not been corrected. Significant cardiovascular impairment within 12 months of start of treatment such as history of congestive heart failure greater than New York Heart Association (NYHA) Class II, unstable angina, myocardial infarction or stroke within 6 months of start of treatment, or cardiac arrhythmia requiring medical treatment at screening. Prolongation of QTc interval to > 480 ms. Left ventricular ejection fraction (LVEF) below the institutional normal range as determined by multigated acquisition scan (MUGA) or echocardiogram (ECHO). Patients who are at risk for severe haemorrhage, bleeding or thrombotic disorders, or are receiving factor X inhibitors or anticoagulants that require therapeutic INR monitoring e.g. warfarin or similar agents. The degree of tumour invasion/infiltration of major blood vessels should be considered because of the potential risk of severe haemorrhage associated with tumour shrinkage/necrosis following lenvatinib therapy. Patients 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. Patients who have not recovered adequately from any toxicity from other anti- cancer treatment regimens and/or complications from major surgery prior to starting therapy. Has had major surgery to the liver prior to start of treatment. Note: If patient received any major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment. Has had a minor surgery (i.e., simple excision) within 7 days prior to start of treatment (Cycle 1 Day 1). Has a serious non-healing wound, ulcer, or bone fracture. History of human immunodeficiency virus (HIV) infection. Has an active infection requiring systemic therapy, with the exception of HBV, HCV. Has severe hypersensitivity (≥Grade 3) to pembrolizumab or lenvatinib and/or any of their excipients. Has dual active HBV infection (HBsAg (+) and /or detectable HBV DNA) and HCV infection (anti-HCV Ab (+) and detectable HCV RNA) at study entry. Has dual active HBV infection and hepatitis D virus (HDV) at the study entry. Has a known history of active tuberculosis (Bacillus tuberculosis). Has a known psychiatric or substance abuse disorder that would interfere with the patient's ability to cooperate with the requirements of the study. Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study intervention. Note: Patients who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent. Has had an allogenic tissue/solid organ transplant. Women who are pregnant or breast feeding. Must be willing to use effective contraception during study and for 120 days after the last dose. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator.