This clinical trial compares the effect of pulmonary vein-first surgical technique to pulmonary artery-first surgical technique in decreasing circulating tumor cell deoxyribonucleic acid (ctDNA) in patients with stage I-III non-small cell lung cancer. Pulmonary vein first and pulmonary artery first surgical techniques are standard surgical techniques for the division of the blood vessels during lung resection surgery. Pulmonary vein-first surgical technique may reduce the risk of shedding tumor cells during surgery and influence long term overall survival.