This study is conducted in two phases. The Dose-finding Lead-in Phase, Part A, will evaluate the safety and determine the maximum tolerated dose (MTD) of momelotinib (MMB) when combined with trametinib. Once the MTD of MMB is determined, the study will proceed to the Dose-finding Lead-in Phase, Part B, to determine the MTD of trametinib. After the MTD is established, the study may proceed to an expansion phase to determine the efficacy, safety, and tolerability of MMB combined with trametinib at the MTD in participants with kirsten rat sarcoma viral oncogene homolog (KRAS) mutated metastatic non-small cell lung cancer (NSCLC). Each treatment cycle will consist of 28 days and treatment will continue in the absence of disease progression, unacceptable toxicity, consent withdrawal, or participant's refusal of treatment.