The goal of Part 1 of this clinical research study is to find the highest dose of (Imbruvica) ibrutinib that can be given to patients with non-small cell lung cancer (NSCLC). The goal of Part 2 of this clinical research study is to learn if the dose of ibrutinib found in Part 1 can help to control the disease.

The safety of this drug will also be studied in both parts of the study.

Study Groups:

If you are found to be eligible to take part in this study, you will be assigned to a study group based on when you join this study. Up to 4 groups of up to 6 participants will be enrolled in Part 1 of the study, and up to19 participants will be enrolled in Part 2.

If you are enrolled in Part 1, the dose of ibrutinib you receive will depend on when you join this study. The first group of participants will receive the lowest dose level of ibrutinib. Each new group will receive a higher dose of ibrutinib than the group before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose of ibrutinib is found.

If you are enrolled in Part 2, you will receive ibrutinib at the highest dose that was tolerated in Part 1.

Study Drug Administration:

You will take ibrutinib pills 1 time each day, at about the same time every day. You may take your dose of ibrutinib with or without food.

Study Visits:

Each cycle is 4 weeks.

On Day 1 of all cycles:

• You will have a physical exam
• Blood (about 3 teaspoons) will be drawn for routine tests.
• On Cycle 2 only, blood (about 1 teaspoon each time) will be drawn for pharmacokinetic (PK) testing before your dose and then 4 more times over the next 6 hours after your dose. PK testing measure the amount of study drug in the body at different timepoints.
• If you the doctor thinks it is needed, blood (about ½ teaspoon) or urine will be collected for pregnancy testing.

Every 8 weeks, you will have a CT, MRI, or x-ray to check the status of the disease. You will have the same type of scan performed as you did at screening.

Length of Study:

You may continue taking the study drug for as long as the doctor thinks it is in your best interest. You will no longer be able to take the study drug 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.

End-of-Dosing Visit:

About 30 days after your last dose of study drug:

• You will have a physical exam.
• Blood (about 3 teaspoons) will be drawn for routine tests.
• If you the doctor thinks it is needed, blood (about ½ teaspoon) or urine will be collected for pregnancy testing.

Follow Up Visits:

Every 6 months you will be asked to come into the clinic or you will be called by a member of the study staff to ask how you are doing and if you have started any new anti-cancer treatments. If you are called, it should take about 10 minutes.

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. The study doctor can explain how the study drug is designed to work.

Up to 43 participants will be enrolled on this study. All will take part 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 Response Evaluation Criteria in Solid Tumors(RECIST) 1.1 criteria
3. For EGFR mutant cohort, patients must have: a) Documented EGFR mutation by Clinical Laboratory Improvement Amendments (CLIA)-certified test b) Documented disease progression on treatment with erlotinib, gefitinib, afatinib, or other EGFR-targeted tyrosine kinase inhibitor c) Tissue available from a biopsy or surgical procedure performed after progression on an EGFR targeted tyrosine kinase inhibitor. If tissue is not available, the patient must have biopsy accessible disease and must be willing to undergo a biopsy.
4. For HER2 mutant cohort, patients must have: a) Documented EGFR mutation by CLIA-certified test b)Documented disease progression on treatment with erlotinib, gefitinib, afatinib, or other EGFR-targeted tyrosine kinase inhibitor c)Tissue available following progression on most recent systemic therapy. If tissue is not available, the patient must have biopsy accessible disease and must be willing 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 normal organ and marrow function as defined: leukocytes >/= 3,000/mcL; absolute neutrophil count >/= 1,500/mcL; hemoglobin >/= 9 g/dL; total bilirubin </= 1.5 x institutional upper limit of normal (ULN); AST(SGOT)/ALT(SGPT) </= 2.5 × ULN or </= 5 x ULN if metastases to the liver; creatinine clearance >/= 45 mL/min
9. Patients with asymptomatic brain metastases are allowed, as long as they are stable and do not require treatment with anticonvulsants or escalating doses of steroids. Maximum daily dose of steroids should be prednisone 20 mg or equivalent. Radiation therapy for brain metastases must be completed at least 14 days prior to treatment on protocol
10. The effects of ibrutinib on the developing human fetus are unknown. Women of child-bearing potential and men must agree to use highly effective contraception (if using hormonal birth control must add a second barrier method; abstinence) prior to study entry, for the duration of study participation as well as for at least 1 month after the last dose of ibrutinib. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use highly effective contraception prior to the study, for the duration of study participation and 3 months after completion of ibrutinib administration.
11. Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

1. Patients who have received EGFR tyrosine kinase inhibitors within 72 hours of initiation of study treatment, or treatment with other anti-cancer agents within 21 days of study treatment
2. Prior treatment with ibrutinib
3. Known hypersensitivity to ibrutinib
4. Concurrent use of agents that strongly inhibit or induce CYP3A unless use is approved by the medical monitor
5. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
6. Pregnant and nursing women
7. 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
8. Any gastrointestinal disorder expected to limit absorption of ibrutinib
9. Treatment with warfarin or other vitamin K antagonist. Patients with using warfarin who switch to another form of anticoagulation will be eligible
10. Patients with persistent and uncontrolled atrial fibrillation.

From the first dose through 30 days after the last dose of study medication, up to 2 years