The purpose of this study is to compare the effects on participants' and liver cancer by adding a drug that is used on its own to treat this disease to a combination of two other drugs which is also used to treat liver cancer, compared to the two-drug combination alone.

An earlier clinical trial showed that a single drug treatment for liver cancer helped stabilize or shrink participants' liver cancer and extend the time before their cancer got worse. A different clinical trial showed that a different two-drug combination helped extend how long participants with liver cancer lived after starting the treatment. Combinations of drugs that are similar to these treatments have been studied in a few people and seem promising, but it is not clear if the combination of all three drugs being used in this study can offer better results than standard treatment.

Inclusion Criteria:

• Age ≥ 18 years.
• Body weight > 30 kg.
• Life expectancy of at least 12 weeks.
• Confirmed HCC based on histopathological findings from tumour tissues or clinically by AASLD criteria in cirrhotic participants.
• Must not have received prior systemic therapy for HCC.
• Must not be eligible for locoregional therapy for unresectable HCC. For patients who progressed after locoregional therapy for HCC, locoregional therapy must have been completed ≥28 days prior to the baseline scan of the abdomen and pelvis for the current study.
• Barcelona Clinic Liver Cancer (BCLC) stage B (that is not eligible for locoregional therapy) or stage C.
• Child-Pugh Score class A or B7 based on low albumin (albumin 25-27 g/L) only.
• Must have Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
• At least 1 measurable lesion, not previously irradiated, that can be accurately measured at baseline as ≥10 mm in the longest diameter (except lymph nodes, which must have a short axis ≥15 mm) with computerized tomography (CT) or magnetic resonance imaging (MRI), and that is suitable for accurate repeated measurements as per RECIST 1.1 guidelines. A lesion which progressed after previous ablation or TACE could be measurable if it meets these criteria.
• Participants with active HBV infection [characterized by positive hepatitis B virus surface antigen (HBsAg) and/or positive hepatitis B core antibodies (anti-HBcAb) with detectable HBV deoxyribonucleic acid (DNA) (≥10 IU/mL or above the limit of detection per local lab standard)] are eligible if:
• The participant is being treated with antiviral therapy, as per institutional practice. The HBV antiviral therapy must be initiated prior to randomization, and the participant must remain on antiviral therapy for the study duration and for 6 months after the last dose of study medication.
• The participant must show evidence of HBV stabilization or signs of viral response (eg, reduction of HBV DNA levels) prior to enrollment
• Participants who test positive for HBsAg or anti-hepatitis B core (HBc) with undetectable HBV DNA (< 10 IU/mL or under the limit of detection per local lab standard) are eligible and do not require antiviral therapy prior to randomization.
• These participants will be tested at every cycle to monitor HBV DNA levels and initiate antiviral therapy if HBV DNA is detected (≥ 10 IU/mL or above the limit of detection per local lab standard).
• If HBV DNA becomes detectable during study treatment, antiviral therapy must be initiated, and the participant must remain on antiviral therapy during the study treatment period and for 6 months after the last dose of study medication.
• Participants with active HCV infection (as characterized by the presence of detectable HCV ribonucleic acid [RNA] or anti-HCV antibody [anti-HCV]) must be managed per local institutional practice for the study and for 6 months after the last dose of study treatment.
• Adequate organ and marrow function, within 14 days prior to enrollment.
• Participants of childbearing potential must have agreed to use a highly effective contraceptive method from enrollment to 90 days after the last dose of durvalumab or 180 days after the last dose of tremelimumab (whichever date is later).
• Participants must agree not to donate blood for at least 90 days following the last infusion of durvalumab or tremelimumab, or until 7 days after the last dose of lenvatinib, whichever is longest.

Exclusion Criteria:

• Participants with a history of other malignancies, except: adequately treated non-melanoma skin cancer, curatively treated in-situ cancer of the cervix, or other tumours curatively treated with no evidence of disease for ≥ 5 years.
• Any concurrent chemotherapy, study drug, or biologic or hormonal therapy for cancer treatment. Concurrent use of hormonal therapy for non-cancer-related conditions (e.g., hormone replacement therapy) is acceptable.
• Known fibrolamellar HCC, sarcomatoid HCC, infiltrative-type HCC or mixed cholangiocarcinoma and HCC.
• Clinically meaningful ascites, defined as ascites requiring non-pharmacologic intervention
• Uncontrolled arterial hypertension defined by a systolic pressure ≥ 150 mm Hg or diastolic pressure ≥ 90 mm Hg or other hypertensive cardiovascular complications despite standard medical management.
• Any previous treatment with a PD1 or PD-L1 inhibitor, including durvalumab, or an anti-CTLA4, including tremelimumab.
• History of primary immunodeficiency, history of organ transplant or prior history of severe (grade 3 or 4) immune mediated toxicity from other immune therapy.
• Known to have tested positive for human immunodeficiency virus (HIV) (positive HIV 1/2 antibodies) or active tuberculosis infection (clinical evaluation that may include clinical history, physical examination and radiographic findings, or tuberculosis testing in line with local practice).
• Known allergy or hypersensitivity to any of the study drugs or any of the study drug excipients.
• Current or prior use of immunosuppressive medication within 28 days before the first dose of durvalumab or tremelimumab
• Active or prior documented autoimmune or inflammatory disorders including inflammatory bowel disease (e.g. Crohn's disease, ulcerative colitis), diverticulitis (with the exception of diverticulosis), systemic lupus erythematosus, Sarcoidosis syndrome, or Wegener syndrome (granulomatosis with polyangiitis), Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc.
• Patients with active or uncontrolled intercurrent illness
• History of leptomeningeal carcinomatosis.
• Symptomatic or uncontrolled brain metastases requiring concurrent treatment, inclusive of but not limited to surgery, radiation and/or corticosteroids.
• Major surgical procedure (as defined by the Investigator) within 28 days prior to enrollment.
• Mean QT interval corrected for heart rate using Fridericia's formula (QTcF) ≥470 ms calculated from 3 ECGs (within 15 minutes at 5 minutes apart).
• Receipt of live attenuated vaccination (examples include, but are not limited to, vaccines for measles, mumps, and rubella, live attenuated influenza vaccine (nasal), chicken pox vaccine, oral polio vaccine, rotavirus vaccine, yellow fever vaccine, BCG vaccine, typhoid vaccine and typhus vaccine) within 30 days prior to enrollment.
• Lactating participants.
• Any active disease condition which would render the protocol treatment dangerous or impair the ability of the patient to receive protocol therapy.
• Receipt of radiotherapy within four weeks of first planned dose of durvalumab or tremelimumab, except for a single dose of radiation up to 8 Gray (equal to 800 RAD) delivered with palliative intent for pain control up to 14 days before enrollment.
• Active or prior documented GI bleeding (e.g. esophageal varices or ulcer bleeding) within 6 months. (Note: For patients with a history of GI bleeding more than 6 months prior or assessed as high risk for esophageal varices by the Investigator or main trunk portal vein thrombosis (Vp4), adequate endoscopic assessment and treatment of varices as per institutional standards is required prior to enrollment.)