The goal of this clinical research study is to learn if Imbruvica (ibrutinib) alone and then in combination with Opdivo (nivolumab) can control NSCLC in patients who have received previous chemotherapy treatment.

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.

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.