Palbociclib is an oral drug which has been shown to stop the cell cycle, which is the way a cell initiates growth. Binimetinib is also an oral drug which stops a signal that a cell receives, instructing it to grow. By putting these two drugs together the investigators hope that it will have a greater affect on cancer growth than either drug alone. The FDA (the U.S. Food and Drug Administration) has not approved binimetinib as a treatment for any disease. The FDA has not approved palbociclib for use in lung cancer but it has been approved for other cancer types.