Additional Study Information: The purpose of this study is to gain a better understanding of why some patients with non-small cell lung cancer and an epidermal growth factor receptor (EGFR-sensitizing mutation, fail first-line treatment with the drug osermitinib. Additionally, the purpose is to explore different drug therapies for patients whose cancer has progressed (gotten worse) after treatment with osermitinib, and to evaluate each therapy safety and how effective each is at treating cancer. Each patient will be evaluated for mutations that might have made them resistant to osermitinib. Patients with certain mutations will be placed in Groups A and B and will be assigned to an appropriate treatment option. Patients who do not meet eligibility criteria for the trial will be placed into an observational group where no study drugs will be received and no study procedures will be done.