A Trial of Gefitinib in Combination With BKM120 in Patients With Advanced Non-Small Cell Lung Cancer, With Enrichment for Patients Whose Tumours Harbour Molecular Alterations of PI3K Pathway and Known to Overexpress EGFR

Inclusion Criteria: 1. Two patient groups are eligible for enrolment. Either: * Patients with histologically or cytologically proven NSCLC who meet the clinical definition of EGFR TKI resistance, and are progressing on existing treatment or have previously progressed on EGFR TKI (Patient Group 1 "EGFR TKI Resistant") * Enrichment Cohort (Patient Group 2 "Pathway Driven Group") Activated PI3K status (Section 7.1) in patients whose tumours are known historically to overexpress EGFR. Patients permitted in this group are those in whom no standard treatment options are available. 2. Age \</= 21 years 3. WHO performance status \</= 2 4. Patients must have at least one site of measurable disease \[only in dose expansion phase\] (per RECIST for solid tumors or the appropriate disease classification/criteria for the target population) 5. Life expectancy of \</= 12 weeks 6. Adequate bone marrow function as shown by: ANC 1.0 x 109/L, Platelets 100 x 109/L, Hb \>9 g/dL 7. Adequate coagulation profile with INR \< 2 8. Total calcium (corrected for serum albumin) within normal limits (bisphosphonate use for malignant hypercalcemia control is not allowed) 9. Magnesium \> the lower limit of normal 10. Alanine aminotransferase (ALT) and aspirate aminotransferase (AST) within normal range (or 3.0 ULN if liver metastases are present) 11. Serum bilirubin within normal range ( or 1.5 x ULN if liver metastases are present; or total bilirubin 3.0 x ULN with direct bilirubin within normal range in patients with well documented Gilbert Syndrome 12. Serum creatinine 1.5 x ULN or 24-hour clearance 50 mL/min 13. Serum amylase \< ULN 14. Serum lipase \< ULN 15. Fasting plasma glucose \< 120 mg/dL (6.7 mmol/L) 16. Negative serum pregnancy test within 48 hours before starting study treatment in women with childbearing potential 17. Signed informed consent Exclusion Criteria: 1. Patients who have received prior treatment with a PI3K inhibitor. 2. Patients with a known hypersensitivity to BKM120 or to its excipients 3. Patients with symptomatic brain metastases are excluded. However, patients with metastatic CNS tumors that are controlled and asymptomatic may participate in this trial, if the patient is \> 4 weeks from therapy completion (incl. radiation and/or surgery), or is clinically stable at the time of study entry and is not receiving chronic corticosteroid therapy for CNS metastases 4. Patients with acute or chronic liver, renal disease or pancreatitis 5. Patients with the following mood disorders as judged by the Investigator or a psychiatrist, or as result of patient's mood assessment questionnaire: i. medically documented history of or active major depressive episode, bipolar disorder (I or II), obsessive-compulsive disorder, schizophrenia, a history of suicidal attempt or ideation, or homicidal ideation (immediate risk of doing harm to others) ii. CTCAE grade 3 anxiety iii. meets the cut-off score of 10 in the PHQ-9 or a cut-off of 15 in the GAD-7 mood scale, respectively, will be excluded from the study unless overruled by the psychiatric assessment. iv. selects a positive response of '1, 2, or 3' to question number 9 regarding potential for suicidal thoughts ideation in the PHQ-9 (independent of the total score of the PHQ-9) Note: The psychiatric judgment overrules the mood assessment questionnaire result/investigators judgment. 6. Patients with diarrhea \< CTCAE grade 2 7. Any of the following concurrent severe and/or uncontrolled medical conditions which could compromise participation in the study: i. ST depression or elevation of \< 1.5 mm in 2 or more leads ii. Congenital long QT syndrome iii. History or presence of ventricular arrhythmias or atrial fibrillation iv. Clinically significant resting bradycardia (\< 50 beats per minutes) v. QTc \> 480 msec on screening ECG vi. Complete left bundle branch block vii. Right bundle branch block + left anterior hemiblock (bifascicular block) viii. Unstable angina pectoris \< 6 months prior to starting study drug ix. Acute myocardial infarction \< 6 months prior to starting study drug x. Other clinically significant heart disease such as congestive heart failure requiring treatment (NYHA Class III or IV) or uncontrolled hypertension (please refer to WHO-ISH guidelines) 8. Patients with uncontrolled diabetes mellitus or steroid-induced diabetes mellitus 9. Other concurrent severe and/or uncontrolled concomitant medical conditions (e.g., active or uncontrolled infection) that could cause unacceptable safety risks or compromise compliance with the protocol 10. Impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of BKM120 (e.g., ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection). Patients with unresolved diarrhea will be excluded as previously indicated 11. Patients who have been treated with any hematopoietic colony-stimulating growth factors (e.g., G-CSF, GM-CSF) 2 weeks prior to starting study drug. Erythropoietin or darbepoetin therapy, if initiated at least 2 weeks prior to enrollment, may be continued 12. Patients who are currently receiving treatment with medication that has the potential to prolong the QT interval or inducing Torsades de Pointes and the treatment cannot either be discontinued or switched to a different medication prior to starting study drug 13. Patients who have received corticosteroids 2 weeks prior to starting study drug. Topical and systemic corticosteroids should not be administered with BKM120 14. Patients receiving chronic treatment with steroids or another immunosuppressive agent. 15. Patients who are currently treated with drugs known to be moderate and strong inhibitors or inducers of isoenzyme CYP3A, and the treatment cannot be discontinued or switched to a different medication prior to starting study drug. Please refer to Table 3-5 for a list of moderate to strong inhibitors of CYP3A4 (Please note that co-treatment with weak inhibitors of CYP3A4 is allowed). 16. Patients who have received chemotherapy or targeted anticancer therapy 4 weeks (6 weeks for nitrosourea, antibodies or mitomycin-C) prior to starting study drug or who have not recovered from side effects of such therapy 17. Patients who have received any continuous or intermittent small molecule therapeutics (excluding monoclonal antibodies) or 5 effective half lives prior to starting study drug or who have not recovered from side effects of such therapy 18. Patients who have received wide field radiotherapy 4 weeks or limited field radiation for palliation 2 weeks prior to starting study drug or who have not recovered from side effects of such therapy 19. Patients who have undergone major surgery 4 weeks prior to starting study drug or who have not recovered from side effects of such therapy 20. Patients who are currently taking therapeutic doses of warfarin sodium or any other coumadin-derivative anticoagulant. 21. Women who are pregnant or breast feeding or adults of reproductive potential not employing an effective method of birth control. Double barrier contraceptives must be used through the trial by both sexes. Oral, implantable, or injectable contraceptives may be affected by cytochrome P450 interactions, and are therefore not considered effective for this study. Women of child-bearing potential, defined as sexually mature women who have not undergone a hysterectomy or who have not been naturally postmenopausal for at least 12 consecutive months (i.e., who has had menses any time in the preceding 12 consecutive months), must have a negative serum pregnancy test \< 48 hours prior to initiating treatment 22. Known diagnosis of human immunodeficiency virus (HIV) infection 23. History of another malignancy within 3 years, except cured basal cell carcinoma of the skin or excised carcinoma in situ of the cervix 24. Patient is unable or unwilling to abide by the study protocol or cooperate fully with the investigator