A Study of Ramucirumab (LY3009806) Versus Placebo in Participants With Hepatocellular Carcinoma and Elevated Baseline Alpha-Fetoprotein

Inclusion Criteria: * A diagnosis of HCC based on histopathologic findings, or a diagnosis of cirrhosis and a tumor with classical HCC imaging characteristics. * Sorafenib was the only systemic therapy for HCC and was discontinued for disease progression or intolerance (Main Global and MEE Cohorts only). * The participant received ≤2 prior systemic therapy regimen, excluding prior sorafenib or chemotherapy, for the treatment of HCC (OLE Cohort only). * ≥1 measurable lesion per Response Evaluation Criteria In Solid Tumors (RECIST) Version 1.1 that has not been previously treated with locoregional therapy. A participant with a lesion(s) that has previously been treated with locoregional therapy is also eligible, if the lesion has documented progression after locoregional treatment and is measureable. * Child-Pugh score \<7 (Child-Pugh Class A). * Barcelona Clinic Liver Cancer (BCLC) Stage C disease or BCLC Stage B disease not amenable to locoregional therapy or refractory to locoregional therapy. * Baseline AFP ≥400 nanograms/milliliter. * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * Resolution of all clinically significant toxic effects of prior therapy. * Total bilirubin ≤1.5 times upper limit of normal value (ULN), aspartate transaminase (AST) and alanine transaminase (ALT) ≤5 × ULN. * Creatinine clearance ≥60 milliliters/minute. * Urinary protein is ≤1+ on dipstick or routine urinalysis or 24-hour urine demonstrating \<1 gram of protein. * Absolute neutrophil count ≥1.0 × 10\^9/Liter, hemoglobin ≥9 grams/deciliter, and platelets ≥75 × 10\^9/Liter. * International Normalized Ratio (INR) ≤1.5 and a partial thromboplastin time (PTT) ≤5 seconds above the ULN. * Surgically sterile, postmenopausal, or compliant with a highly effective contraceptive method. * If a woman of childbearing potential, a negative serum pregnancy test prior to randomization. * Willing to provide blood for research. The participant has provided signed informed consent prior to any study specific procedures and is amenable to compliance with protocol schedules and testing. Exclusion Criteria: * Fibrolamellar carcinoma or mixed hepatocellular cholangiocarcinoma. * Concurrent malignancy. Participants with carcinoma in situ of any origin and participants with prior malignancies in remission may be eligible with sponsor approval. * Previous brain metastases, leptomeningeal disease, or uncontrolled spinal cord compression. * History of or current hepatic encephalopathy or clinically meaningful ascites. * Ongoing or recent hepatorenal syndrome. * Liver transplant (Main Global and MEE cohorts only; Participants with prior liver transplant may be eligible for OLE cohort). * Hepatic locoregional therapy following prior systemic therapy or within 28 days prior to randomization. * Major surgical procedure, traumatic injury, non-healing wound, or peptic ulcer ≤28 days prior to randomization. * Received radiation to any nonhepatic (for example, bone) site within 14 days prior to randomization. * Placement of a subcutaneous venous access device within 7 days prior to the first dose of study treatment unless the procedure is judged of low risk of bleeding. * Enrolled in a clinical trial involving an investigational product or unapproved use of a drug or in medical research judged not to be scientifically or medically compatible with this study. * Discontinued from study treatment from another clinical trial within 28 days prior to randomization. * Known allergy to any of the treatment components. * Uncontrolled hypertension. * Any arterial thrombotic event, including myocardial infarction, unstable angina, cerebrovascular accident, or transient ischemic attack, \<6 months prior to randomization. * Any bleeding episode considered life-threatening, or any Grade 3 or 4 gastrointestinal bleeding episode in the 3 months prior to randomization requiring intervention. * Esophageal or gastric varices that require intervention or represent high bleeding risk. Participants with evidence of portal hypertension or prior bleeding must have had endoscopic evaluation within 3 months prior to randomization. * Gastrointestinal perforation or fistulae within 6 months prior to randomization. * Symptomatic congestive heart failure (New York Heart Association II-IV), unstable angina pectoris, or symptomatic or poorly controlled cardiac arrhythmia. * Pregnant or breast-feeding. * Any medical or psychiatric condition that may increase the risk associated with study participation or may interfere with the interpretation of study results. Conditions include but are not limited to: * Human immunodeficiency virus infection or acquired immunodeficiency syndrome-related illness. * Active or uncontrolled clinically serious infection. (Participants with chronic viral hepatitis are eligible.) * Ongoing or recent history of drug abuse. * Uncontrolled hereditary or acquired thrombotic or bleeding disorder. * Bowel obstruction, history or presence of inflammatory enteropathy or extensive intestinal resection. * Therapeutic dose anticoagulation with warfarin, low molecular-weight heparin, or similar agents. * Chronic therapy with nonsteroidal anti-inflammatory agents or other anti-platelet agents. Aspirin at doses up to 100 milligrams/day is permitted. * The participant received prior immunotherapy and is experiencing or has experienced any of the following (OLE cohort only): * Any clinically significant Grade ≥3 immune-related adverse event (irAE) * Any grade neurologic or ocular irAE * Any grade immune-related pneumonitis, cardiomyopathy, or hepatitis * The participant received prior immunotherapy and at the time of study enrollment, requires steroids or other immunosuppressive agents (OLE cohort only).