A Study of Ramucirumab (LY3009806) Given by Injection Under the Skin in Participants With Advanced Cancer

Inclusion Criteria: * Have evaluable disease per Response Evaluation Criteria in Solid Tumors version 1.1 (RECIST 1.1). * In the judgment of the investigator, be an appropriate candidate for experimental therapy and: * For Cohort A only: Have exhausted all anticancer treatments with proven clinical benefit OR * For Cohorts B and C only: Must have one of the three conditions below: * Have exhausted all anti-cancer treatments with proven clinical benefit, OR * Have hepatocellular carcinoma or gastric cancer who have received prior treatment, and where IV ramucirumab monotherapy is clinically acceptable treatment after progression OR * Have a diagnosis for which IV ramucirumab in combination with additional anticancer therapy is clinically acceptable treatment * Additionally, it must be clinically acceptable to delay initiation of the combination partner for 3 weeks from the initiation of ramucirumab dosing. * Eastern Cooperative Oncology Group performance status score of 0 or 1. * Have discontinued all previous treatments for cancer with adequate wash-out period and recovered from the acute effects of therapy. * Have adequate hematologic, hepatic, and renal functions and electrolytes. * Males and females of child-bearing potential must agree to use highly effective contraceptive methods during study treatment and for at least 84 days/12 weeks following the last dose of study drug. Exclusion Criteria: * Have uncontrolled hypertension defined as systolic blood pressure (BP) \>150 mmHg or diastolic BP \>90 mmHg despite standard medical management. * Have significant bleeding disorders or experienced Grade 3/4 gastrointestinal (GI) bleeding within 3 months prior to enrollment. * Have hepatic impairment (such as severe liver cirrhosis Child-Pugh B \[or worse\], cirrhosis with a history of hepatic encephalopathy, clinically meaningful ascites requiring ongoing treatment with diuretics and/or paracentesis, or history of hepatorenal syndrome). * Have experienced any arterial thromboembolic events (ATEs), including but not limited to myocardial infarction, transient ischemic attack, cerebrovascular accident, or unstable angina, ≤6 months prior to randomization. * The participant has clinically relevant congestive heart failure (CHF; New York Heart Association \[NYHA\] Grade ≥2) or symptomatic or poorly controlled cardiac arrhythmia. * Have symptomatic central nervous system (CNS) metastases. Screening is not required. * Have history of GI perforation and/or fistula within 6 months prior to enrollment. * Have an active uncontrolled systemic bacterial, viral, or fungal infection or serious ongoing uncontrolled intercurrent illness. * Have a serious or non-healing wound, ulcer, or bone fracture within 4 weeks prior to enrollment. * Have received IV ramucirumab in the past.