Targeted Therapy in Treating Patients With Incurable Non-Small Cell Lung Cancer With Genetic Mutations

PRIMARY OBJECTIVES: I. To estimate the objective response rate among patients with high PD-L1 expressing cancers after failure of targeted therapy. SECONDARY OBJECTIVES: I. To compare the overall survival for patients receiving treatment targeting primary mutations, secondary mutations, or immunotherapy at the time of progression on tyrosine kinase inhibitor therapy. II. To assess the incidence of secondary mutations in this population according to smoking status. III. To evaluate the response rates of patients treated using these different approaches. IV. To correlate outcomes with specific secondary genetic changes. OUTLINE: Patients are assigned to 1 of 3 treatment arms. ARM I (PD-L1 \>= 50%): Patients receive nivolumab intravenously (IV) over 60 minutes every 2 weeks or pembrolizumab IV every 3 weeks in the absence of disease progression or unacceptable toxicity. ARM II (PD-L1 \< 50% without secondary oncogenic driver): Patients receive tyrosine kinase inhibitor therapy orally (PO) targeting the initial oncogenic driver or other treatment for about 3 weeks. ARM III (PD-L1 \< 50% with secondary oncogenic driver): Patients receive tyrosine kinase inhibitor therapy PO targeting initial oncogenic driver, a drug targeting the secondary mutation, or other treatment for about 3 weeks. After completion of study treatment, patients are followed up for a minimum of 30 days.