The main purpose of this study is to evaluate the efficacy and safety of ramucirumab in combination with erlotinib as compared to placebo in combination with erlotinib in previously untreated participants with stage IV non-small cell lung cancer (NSCLC) harboring an activating epidermal growth factor receptor (EGFR) mutation (Exon 19-Del and Exon 21 L858R). Safety and tolerability of ramucirumab in combination with erlotinib will be assessed in Part A before proceeding to Part B. The purpose of Part C is to determine the efficacy and safety of ramucirumab in combination with gefitinib in previously untreated East Asian participants with EGFR mutation-positive metastatic NSCLC and of ramucirumab in combination with osimertinib in those participants whose disease progressed on ramucirumab and gefitinib and that have T790M - positive metastatic NSCLC.