Trametinib and Docetaxel in Treating Patients With Recurrent or Stage IV KRAS Mutation Positive Non-small Cell Lung Cancer

PRIMARY OBJECTIVES: I. To evaluate the response rate (confirmed and unconfirmed) to trametinib plus docetaxel in the entire study population of Kirsten rat sarcoma viral oncogene homolog (KRAS) mutation positive non-small cell lung cancer (NSCLC) patients following one or two prior systemic therapies. SECONDARY OBJECTIVES: I. To evaluate if trametinib plus docetaxel is consistent with promise of activity measured by the response rate in G12C KRAS mutation positive NSCLC patients following one or two prior systemic therapies. II. To assess the response rate of this combination in non-G12C KRAS mutation positive NSCLC patients. III. To assess progression-free survival within the G12C and non-G12C KRAS positive subgroups and the entire study population. IV. To evaluate the toxicity of the regimen. V. To assess overall survival within G12C positive patients, non-G12C positive patients, and the entire study population. TRANSLATIONAL MEDICINE OBJECTIVES: I. To evaluate the response rates in the presence of comutations p53 and LKB1. II. To bank specimens for future research. OUTLINE: Patients receive trametinib orally (PO) on days 1-21. Patients also receive docetaxel intravenously (IV) on day 1. Cycles repeat every 21 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up every 6 months for 3 years.