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

Inclusion Criteria: * DISEASE RELATED CRITERIA: Patients must have pathologically confirmed KRAS mutation (at codon 12, 13 and 61) positive non-small cell lung cancer (NSCLC) that is stage IV or recurrent; the specific subtype of KRAS mutation must be known; KRAS mutation testing must have been performed in a Clinical Laboratory Improvement Act (CLIA) certified laboratory; CLIA certified commercially available tests are acceptable * DISEASE RELATED CRITERIA: Patients must have measurable disease documented by computed tomography (CT) or magnetic resonance imaging (MRI) within 28 days prior to registration; the CT from a combined positron emission tomography (PET)/CT may be used only if it is of diagnostic quality; non-measurable disease must be assessed within 42 days prior to registration; all known sites of disease must be assessed and documented on the baseline tumor assessment form (Response Evaluation Criteria in Solid Tumors \[RECIST 1.1\]) * DISEASE RELATED CRITERIA: Patients must not have known brain metastases, leptomeningeal carcinomatosis or spinal cord compression unless: (1) metastases have been locally treated (including stereotactic body radiation therapy \[SBRT\], whole brain radiotherapy \[WBRT\], and surgical resection) and have remained clinically controlled and asymptomatic for at least 14 days following treatment and prior to registration, AND (2) patient has no residual neurological dysfunction and has been off corticosteroids for at least 2 days prior …