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

Inclusion Criteria: 1. Patients must have histologically or cytologically confirmed stage IV non-small cell lung cancer, or recurrent non-small cell lung cancer which is not amenable to curative intent therapy. 2. Patients must have measurable disease by RECIST 1.1 criteria 3. Patients must have experienced progressive disease following at least one platinum-based chemotherapy regimen in the setting of advanced disease or have progressed within 6 months of receiving chemotherapy as part of loco-regional therapy. 4. Patients must have biopsy accessible disease and must be willing and able to undergo a biopsy 5. Age \>/= 18 years. 6. Eastern Cooperative Oncology Group (ECOG) performance status \</= 2 7. Ability to take pills by mouth 8. Patients must have adequate organ and marrow function as defined below: leukocytes \>/= 3,000/mcL absolute neutrophil count \>/= 1,000/mcL independent of growth factor support platelet count \>/= 100,000/mm3 independent of transfusion support OR \>/= 50,000/mm3 independent of transfusion support if bone marrow involvement total bilirubin \</= 1.5 x institutional upper limit of normal (ULN) unless bilirubin rise is due to Gilbert's syndrome AST(SGOT)/ALT(SGPT) \</= 3 × ULN creatinine clearance \>/= 25 mL/min 9. Patients with asymptomatic brain metastases are allowed, as long as they are treated, stable, and do not require treatment with anticonvulsants or escalating doses of steroids. Maximum daily dose of steroids should be prednisone 10 mg or equivalent. Radiation therapy for brain metastases must be completed at least 14 days prior to treatment on protocol. Patients with untreated brain metastases who are stable, asymptomatic and not requiring treatment with anticonvulsants or escalating doses of steroids are eligible. 10. Women of childbearing potential and men who are sexually active must be practicing a highly effective method of birth control during and after the study consistent with local regulations regarding the use of birth control methods for subjects participating in clinical trials. Men must agree to not donate sperm during and after the study. For females, these restrictions apply for 3 months after the last dose of ibrutinib and 6 month after the last dose of nivolumab. For males, these restrictions apply for 3 month after the last dose of study drugs. 11. Women of childbearing potential must have a negative serum beta-human chorionic gonadotropin (b-hCG)) or urine pregnancy test within 7 days prior to treatment initiation and when clinically indicated every 4 weeks +/- 7 days while receiving study drugs, as shown in study calendar. Women who are pregnant or breastfeeding are ineligible for this study. 12. Sign (or their legally-acceptable representatives must sign) an informed consent document indicating that they understand the purpose of and procedures required for the study, including biomarkers, and are willing to participate in the study. Exclusion Criteria: 1. Patients who have had chemotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study. 2. Prior treatment with ibrutinib, a PD-1 inhibitor, a PD-L1 inhibitor, or a CTLA-4 inhibitor 3. Known hypersensitivity to ibrutinib or nivolumab 4. Major surgery or a wound that has not fully healed within 4 weeks of treatment. 5. Known central nervous system lymphoma 6. History of stroke or intracranial hemorrhage within 6 months prior to treatment. 7. Treatment with warfarin or other vitamin K antagonists. Patients who are on active treatment with warfarin or other vitamin K antagonists for conditions requiring anticoagulation will be switched, when not contraindicated, to a different form of anticoagulation, including low molecular weight heparin (LMWHs) (ex: enoxaparin, dalteparin) or oral anti-Xa drugs (ex: rivaroxaban or apixaban) Patients who switch to these alternative forms of anticoagulation will be eligible. 8. Current or prior use of immunosuppressive medication within 14 days of treatment on protocol, with the exception of intranasal and inhaled corticosteroids or oral corticosteroids at physiological doses, which are not to exceed 10 mg/day of prednisone, or an equivalent corticosteroid. 9. Active or prior documented autoimmune disease within the past 2 years. Patients with a history of vitiligo, Grave's disease, or psoriasis not requiring systemic treatment (within the past 2 years) are not excluded. 10. Active or prior documented inflammatory bowel disease (e.g. Crohn's disease, ulcerative colitis) 11. Known history or previous clinical diagnosis of tuberculosis 12. History of primary immunodeficiency 13. History of organ transplant requiring therapeutic immunosuppression 14. Patients requiring chronic treatment with strong CYP3A inhibitors 15. Clinically significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of Screening, or any Class 3 (moderate) or Class 4 (severe) cardiac disease as defined by the New York Heart Association Functional Classification. 16. Baseline arterial blood pressure (BP) \>/=140/90 mmHg, despite pharmacologic treatment with antihypertensive agents. If the arterial BP measurements at screening are \>/= 140/90 mmHg in a patient not on pharmacologic treatment for hypertension (HTN), we will initiate pharmacologic therapy and reassess the parameters after 1 week. At that time, patient will be eligible for enrollment on the study if arterial BP is found \<140/90 mmHg on antihypertensive therapy. 17. Pregnant and nursing women. 18. Patients with a history of another active malignancy within the past two years, with the exception of non-melanoma cutaneous malignancy, cervical carcinoma in situ, or ductal carcinoma in situ which has been successfully treated with curative intent therapy. 19. Any gastrointestinal disorder expected to limit absorption of ibrutinib 20. Vaccinated with live, attenuated vaccines within 4 weeks of treatment. 21. Known history of human immunodeficiency virus (HIV) or active Hepatitis C Virus or active Hepatitis B Virus infection or any uncontrolled active systemic infection. 22. Any life-threatening illness, medical condition, or organ system dysfunction which, in the investigator's opinion, could compromise the subject's safety, interfere with the absorption or metabolism of ibrutinib capsules, or put the study outcomes at undue risk.