Testing the Timing of Pembrolizumab Alone or With Chemotherapy as First Line Treatment and Maintenance in Non-small Cell Lung Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed stage IV non-squamous non-small cell lung cancer (NSCLC) (includes M1a, M1b, and M1c stage disease, American Joint Committee on Cancer \[AJCC\] 8th edition). Patients with stage IIIB and IIIC disease are eligible if they are not candidates for combined chemotherapy and radiation. Prior chemo-radiation therapy (RT) for stage III with recurrence is allowed * Patients must have PD-L1 expression Tumor Proportion Score (TPS) \>= 1% in tumor cells. If PD-L1 expression TPS is unevaluable or the testing could not be completed, the patients are not eligible. The assay must have been performed by a Clinical Laboratory Improvement Act (CLIA) (or equivalent) certified laboratory * Patients must have measurable or non-measurable disease. The presence of malignant pleural fluid alone is sufficient to satisfy this eligibility criterion. Baseline imaging assessments and measurements used to evaluate all measurable or non-measurable sites of disease must be done within 4 weeks prior to study registration * NOTE: If patient receives pemetrexed, follow institutional guidelines to drain fluids * NOTE: An additional 15 days is allowed to account for any infection/exposure related logistical delays * Patients must be \>= 18 years of age * Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 * Patients must NOT have received the following: * Prior systemic chemotherapy…