This phase III ALCHEMIST trial studies how well erlotinib hydrochloride compared to observation works in treating patients with stage IB-IIIA non-small cell lung cancer that has been completely removed by surgery (resected). Erlotinib hydrochloride may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth.

PRIMARY OBJECTIVE: I. To assess whether adjuvant therapy with erlotinib hydrochloride (erlotinib) will result in improved overall survival (OS) over observation for patients with completely resected stage IB (\>= 4 cm)-IIIA epidermal growth factor receptor (EGFR) mutant non-small cell lung cancer (NSCLC) (confirmed centrally) following complete resection and standard post-operative therapy. SECONDARY OBJECTIVES: I. To assess whether adjuvant therapy with erlotinib will result in improved disease free survival (DFS) over observation for patients with completely resected stage IB (\>= 4 cm)-IIIA EGFR mutant NSCLC (confirmed centrally) following complete resection and standard post-operative therapy, both overall and within the stage subgroups: IB and II/IIIA. II. To evaluate the safety profile of erlotinib in the adjuvant setting. III. To assess whether adjuvant therapy with erlotinib will result in improved DFS rate at 2 years, and OS rate at 5 and 10 years over observation for patients with completely resected stage IB (\>= 4 cm)-IIIA EGFR mutant NSCLC (confirmed centrally) following complete resection and standard post-operative therapy, both overall and within the stage subgroups: IB and II/IIIA. IV. To assess the primary and secondary objectives in all randomized patients, regardless of central confirmation of the EGFR mutant status. V. To study detection of circulating EGFR mutations in cell-free plasma deoxyribonucleic acid (DNA) as a prognostic marker in resected early stage NSCLC. OUTLINE: Patients are randomized to 1 of 4 treatment arms. ARM A (BLINDED ERLOTINIB- CLOSED 06/14/17): Blinded patients receive erlotinib hydrochloride orally (PO) once daily (QD) on days 1-21. Treatment repeats every 21 days for up to 2 years in the absence of disease progression or unacceptable toxicity. ARM B (PLACEBO- CLOSED 06/14/17): Patients receive placebo PO QD on days 1-21. Treatment repeats every 21 days for up to 2 years in the absence of disease progression or unacceptable toxicity. ARM C (UNBLINDED ERLOTINIB): Unblinded patients receive erlotinib hydrochloride PO QD on days 1-21. Treatment repeats every 21 days for up to 2 years in the absence of disease progression or unacceptable toxicity. ARM D (OBSERVATION): Patients (including patients previously randomized to placebo) undergo observation at least every 6 months for 2 years. After completion of study treatment, patients are followed up every 6 months for 4 years and then yearly for 6 years.