This early phase I trial studies the side effects and how well local consolidative therapy (LCT) and brigatinib works in treating patients with non-small cell lung cancer that is stage IV or has come back (recurrent). Giving LCT, such as surgery and/or radiation, after initial treatment may kill any remaining tumor cells. Brigatinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Giving LCT and brigatinib may work better in treating patients with non-small cell lung cancer.