A Study of Ramucirumab (LY3009806) Plus MEDI4736 in Participants With Advanced Gastrointestinal or Thoracic Malignancies

Inclusion Criteria: * Measurable metastatic disease or locally advanced and unresectable disease * Has histopathologically confirmed gastric or GEJ adenocarcinoma with documented disease progression after 1-2 prior lines of systemic therapy * Has histopathologically confirmed nonsquamous or squamous NSCLC with documented disease progression after 1-3 prior lines of systemic therapy * Has histopathologically or cytologically confirmed HCC, Child-Pugh Class A, with documented disease progression during or after discontinuation of sorafenib therapy, or intolerance of sorafenib therapy, and an α-fetoprotein (AFP) ≥ 1.5x upper limit of normal * Availability of tumor tissue for biomarker analysis * Has an Eastern Cooperative Oncology Group Performance Status of 0 or 1 * Has adequate organ function Exclusion Criteria: * Has known brain metastases * Has a history of prior cancers not included in this study that were either not treated with curative intent or have been active within the past 5 years * History of allogeneic organ transplant * Has active or prior documented autoimmune disease within the past 24 months * Has human immunodeficiency virus (HIV) infection or acquired immunodeficiency syndrome (AIDS)-related illness, or a history of immunodeficiency * Has active hepatitis B or hepatitis C infection, or co-infection with both hepatitis B and C virus * For gastric/GEJ and NSCLC participants, has chronic hepatitis B or hepatitis C infection. (For HCC participants, those with chronic hepatitis B virus \[HBV\] infection with a negative HBV deoxyribonucleic acid \[DNA\] test and who are on antiviral therapy, and those with chronic hepatitis C virus \[HCV\] infection are eligible) * Has a history of interstitial lung disease, idiopathic pulmonary fibrosis, pneumoconiosis, non-infections pneumonitis, radiation-induced or drug-induced pneumonitis * Has received any previous systemic therapy targeting programmed death (PD) 1 or PD-ligand 1/2 signaling pathways, and other immune checkpoint inhibitors * Have received previous systemic therapy with ramucirumab