This is an open-label phase I/II multi-center study consisting of two parts. Part A of this study is designed to identify the recommended phase 2 dose (RP2D) of lapatinib combined with trametinib in patients with metastatic KRASm and PIK3CA wild-type (PIK3CAwt) non-small cell lung cancer (NSCLC). Part B is designed to perform a randomized comparison of the lapatinib-trametinib combination versus standard of care therapy in patients with metastatic KRASm/PIK3CAwt NSCLC.