Study of Ibrutinib Followed by Ibrutinib in Combination With Nivolumab in Non-Small Cell Lung Cancer (NSCLC)

Study Drug Administration: Each study cycle will be 28 days. If you are found to be eligible to take part in this study, during Cycle 1, you will take ibrutinib alone. Ibrutinib should be taken by mouth 1 time each day with a glass of water. You should take the study drug at the same time every day. You may take your dose of ibrutinib with or without food. If you miss a dose, take it as soon as possible on the same day with a return to the normal schedule the following day. You should not take any extra doses on the following day to make up for any forgotten doses. Beginning with Cycle 2, you will receive nivolumab by vein over 60 minutes on Days 1 and 15 of every cycle. You will continue to take ibrutinib as you did during Cycle 1. You will be given a pill diary to complete. You should record in the diary each dose of medication you take and when you took it. You should bring this diary with you to each study visit. Study Visits: On Day 1 (+/- 7 days) of all cycles: * You will have a physical exam. * Blood (about 2 teaspoons) will be drawn for routine tests. Between Days 21 and 28 of Cycle 1: * You will have a tumor biopsy for biomarker testing and to check your immune system's response to the study drug. * Blood (about 1-2 teaspoons) will be drawn for cytokine/chemokine testing. On Day 28 of Cycle 1 only, you will have a CT of the neck and chest to check the status of the disease. On Day 28 (+/- 7 days) of Cycle 1 and then every 8 weeks after that: * Blood (about 1 teaspoon) will be drawn to check your thyroid function. * You will have a CT or MRI scan to check the status of the disease. If you can become pregnant, you may have a blood (about 1 teaspoon) or urine pregnancy test at any time the doctor thinks it is needed. Length of Study: You may receive ibrutinib for up to 2 years. You may receive nivolumab for as long as the study doctor thinks it is in your best interest. You will no longer be able to take the study drug(s) if the disease gets worse, if intolerable side effects occur, or if you are unable to follow study directions. Your participation on the study will be over after the follow-up visits. Follow up: Within 30 days after the last dose of study drug: * You will have a physical exam. * Blood (about 1 teaspoon) will be drawn for routine tests. * If you can become pregnant, blood (about 1 teaspoon) or urine will be collected for a pregnancy test. Long-term follow up: Every 6 months for up to 2 years after your first dose of study drug: * You will have a physical exam. * Blood (about 2 teaspoons) will be drawn for routine tests. This is an investigational study. Ibrutinib is FDA approved and commercially available for the treatment of chronic lymphocytic leukemia (CLL) and mantle cell lymphoma (MCL). It is considered investigational to use this drug to treat NSCLC. Nivolumab is FDA approved and commercially available for the treatment of advanced NSCLC. The study doctor can explain how the study drugs are designed to work. Up to 25 participants will be enrolled in this study. All will be enrolled at MD Anderson.