A Study of Emibetuzumab in Combination With Ramucirumab (LY3009806) in Participants With Advanced Cancer

Inclusion Criteria: * Participants must have histological or cytological confirmed diagnosis of the following tumor types that is advanced and/or metastatic cancer and must be, in the judgment of the investigator, an appropriate participant for experimental therapy * Part A: Any type of solid tumor ("all comer") * Part B1: Gastric or Gastroesophageal Junction (GEJ) adenocarcinoma * Part B2: Hepatocellular cancer (excluding fibrolamellar carcinoma) * Part B3: Renal cell carcinoma (any histology) * Part B4: Non-small cell lung cancer (squamous or non-squamous) * Have at least 1 measurable lesion outside of the central nervous system (CNS) whose presence is assessable using standard techniques by Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1. * Availability of a tumor sample taken after progression on the most recent line of systemic tumor therapy or willing to undergo a tumor biopsy pre-study treatment. * Have a performance status of ≤ 2 on the Eastern Cooperative Oncology Group (ECOG) scale in Part A and ≤ 1 on the ECOG scale in Part B. * Have adequate organ function. * Routine urinalysis showing ≤1+ protein or protein/creatinine ratio \<0.5. For proteinuria ≥2+ or urine protein/creatinine ratio ≥0.5, 24-hour urine must be collected and the level must be \<1 gram of protein in 24 hours for subject enrollment. * Have discontinued all previous cancer therapies and any agents that have not received regulatory approval for any indication, for at least 21 days or 5 halflives prior to study enrollment, whichever is shorter, and recovered from the acute effects for therapy. * Have an estimated life expectancy, in the judgment of the investigator, that will permit the participant to complete 8 weeks (2 cycles) of treatment. * Males and females with reproductive potential: Must agree to use medically approved contraceptive precautions during the study and for at least 3 months following the last dose of study drug. Females with childbearing potential must have had a negative serum pregnancy test 7 days before the first dose of study drug and must not be breast-feeding. Exclusion Criteria: * Have serious pre-existing medical conditions (at the discretion of the investigator, such as severe acute or chronic medical condition or laboratory abnormality that may increase the risk associated with study participation). * Have a history of hypertensive crisis or hypertensive encephalopathy or current poorly controlled hypertension despite standard medical management. * Participant has experienced any arterial thromboembolic event (ATE), including myocardial infarction, unstable angina pectoris, cerebrovascular accident, or transient ischemic attack, within 6 months prior to receiving study drugs. * Have a history of deep vein thrombosis, pulmonary embolism, or any other significant thromboembolic event during the 3 months prior to receiving study drugs. * Are receiving therapeutic anticoagulation with warfarin, low-molecular weight heparin, or similar agents. Participants receiving prophylactic, low-dose anticoagulation therapy are eligible provided that they are on low-molecular weight heparin or oral factor Xa inhibitors. * The participant is receiving chronic therapy with nonsteroidal anti-inflammatory drugs or other antiplatelet agents. Aspirin use at doses up to 325 mg/day is permitted. * Have significant bleeding disorders, vasculitis, or had a significant bleeding episode from the gastrointestinal (GI) tract within 3 months prior to receiving study drugs. * Have a history of GI perforation and/or fistulae within 6 months prior to receiving study drugs. * Have congestive heart failure (CHF) New York Heart Association class ≥3 or symptomatic or poorly controlled cardiac arrhythmia. * Have undergone major surgery within 28 days prior to receiving study drugs. * Have a serious or nonhealing wound, peptic ulcer, or bone fracture within 28 days prior to receiving study drugs. * Have a known active fungal, bacterial, and/or known viral infection. Hepatocellular cancer participants with chronic viral (B or C) hepatitis are eligible if they retain adequate liver function. * Have liver cirrhosis with a Child-Pugh Stage of B or C. * Have symptomatic CNS malignancy (with the exception of medulloblastoma) or metastasis. * Have corrected QT (QTc) interval of \>470 milliseconds on screening electrocardiogram (ECG). * Have received previous treatment with ramucirumab or Emibetuzumab, except for participants enrolled in cohort B1 (Gastric or GEJ adenocarcinoma) and B4 (non- small cell lung cancer) who may have received previous ramucirumab treatment. * Known hypersensitivity to any of the treatment components of ramucirumab or Emibetuzumab. * Have a second primary malignancy that, in the judgment of the investigator and sponsor, may affect the interpretation of results. * Are pregnant or breastfeeding. * For Part B4 (non-small cell lung cancer) only: * The participant has radiologically documented evidence of major blood vessel invasion or encasement by cancer * Participants with a history of gross hemoptysis within 2 months prior to study treatment * The participant has radiographic evidence of intratumor cavitation, regardless of tumor histology