Clinical trial on the treatment of persons who are diagnosed with Lung Cancer.

Participants in this study will undergo screening tests and procedures to determine whether you are eligible to participate with the research study. If you meet the requirements to participate with the study, you be given Brigatinib by mouth each day for 7 days. If you do not experience any intolerable side effects while taking Brigatinib, you will receive an increased dose starting on Day 8 and take Brigatinib continuously each day thereafter. Bevacizumab will be given intravenously (IV) on Day 8 in combination with Brigatinib. The first 28 days of treatment is called Cycle 1. Starting Cycle 2 and thereafter, one cycle will consist of 21 days. Bevacizumab will be given on Day 1 every 21 days starting Cycle 2. Participation is expected to last until your disease worsens or you decide you no longer want to participate in the study. There will be a follow-up visit within 30 days of treatment discontinuation. The study team will check in with you every three months after this final visit to see how you are doing. If you decide to take part, this is what will happen: Since we are looking for the highest dose of the study drug that can be administered safely without severe or unmanageable side effects in participants that have Anaplastic Lymphoma Kinase (ALK) Rearranged Non-Small Cell Lung Cancer (NSCLS), not everyone who participates in this research study will receive the same dose of the study drug. The dose you get will depend on the number of participants who have been enrolled in the study before you and how well they have tolerated their doses. If you take part in this research study, you will be given a drug diary. You will be asked to document information in the drug diary about the study drug you are being asked to take. If you take part in this research, study you will be given a study calendar. Information about what to expect during and between study visits will be included in the study calendar.