Study of Selective BRAF Kinase Inhibitor Dabrafenib Monotherapy Twice Daily and in Combination With Dabrafenib Twice Daily and Trametinib Once Daily in Combination Therapy in Subjects With BRAF V600E Mutation Positive Metastatic (Stage IV) Non-small Cell Lung Cancer.

Inclusion Criteria: * Signed written informed consent; * Histologically or cytologically confirmed non-small cell cancer of the lung (NSCLC) stage IV (accordingto AJCC Staging 7th Edition); * For Cohorts A and B, documented tumor progression (based on radiological imaging) after receiving at least one prior approved platinum-based chemotherapy regimen for advanced stage/metastatic NSCLC. An alternate chemotherapeutic agent/regimen is an acceptable substitute in the event that the subject was intolerant to, or ineligible to receive platinum based chemotherapy. Subjects enrolled in Cohort B cannot have more than 3 prior systemic treatments for advanced stage/metastatic NSCLC (neoadjuvant and adjuvant therapies are not counted in number of prior regimens and maintenance therapy is not counted as a separate regimen). Subjects in Cohort C will be required to have not received prior systemic anti-cancer therapies for metastatic disease (i.e., dabrafenib/trametinib will be 1st line treatment for metastatic disease); * Measurable disease according to Response Evaluation Criteria in Solid Tumors \[RECIST 1.1\]; * At least 18 years of age; * Anticipated life expectancy of at least three months; * Presence of a BRAF V600E mutation in lung cancer tissue. Mutation must be locally confirmed in a CLIA-certified laboratory (or equivalent). An adequate amount of tumor tissue (archived tumor tissue, or fresh biopsy if archived tissue is not available) must be available at the time of enrolment for central validation of BRAF mutation; * Able to swallow and retain oral medication; * Women of childbearing potential must have a negative serum pregnancy test within 14 days before the first dose of study treatment and agree to use effective contraception during the study; NOTE: Oral contraceptives are not reliable due to potential drug-drug interaction with dabrafenib. * Eastern Cooperative Oncology Group (ECOG) Performance Status of 0-2; * Must have adequate organ function as defined by the following baseline values: Absolute neutrophil count (ANC) \>/=1.5x10\^9/L Hemoglobin \>/=9 g/dL Platelets \>/=100x10\^9/L Prothrombin time /International normalized ratio (INR) and partial thromboplastin time \</=1.5xULN (Subjects receiving anticoagulation treatment may be allowed to participate with INR established within the therapeutic range prior to starting study treatment.) Total bilirubin \</=1.5 x upper limit of normal (ULN) Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \</= 2.5xULN Serum creatinine \</=1.5 mg/dL (if serum creatinine is \>1.5 mg/dL, calculate creatinine clearance using standard Cockcroft and Gault; creatinine clearance must be \> 50 mL/min); creatinine clearance should be \>/= 50 mL/min Left ventricular ejection fraction \>/= institutional lower limit of normal ECHO * French subjects: In France, a subject will be eligible for inclusion in this study only if either affiliated to or a beneficiary of a social security category * Previously tested for presence of EGFR and ALK mutations in lung cancer tissue confirmed in a CLIA-certified laboratory (or equivalent). Subjects with EGFR or ALK mutation are eligible if they have previously received EGFR or ALK inhibitor(s) respectively. Exclusion Criteria: * Previous treatment with a BRAF inhibitor (including but not limited to dabrafenib, vemurafenib, LGX818, and XL281/BMS-908662) or MEK inhibitor (including but not limited to trametinib, AZD6244, and RDEA119) prior to start of study treatment (Note: Prior treatment with dabrafenib is allowed for crossover subjects in Cohort A); * Anti-Cancer therapy including chemotherapy, radiation-therapy, immunotherapy, biologic therapy or major surgery within 14 days prior to start of study treatment (Note: Dabrafenib monotherapy within 14 days prior to starting combination therapy is allowed for crossover subjects in Cohort A); * Use of any investigational anti-cancer drug within 14 days or 5-half-lives (minimum 14 days), prior to start of study medication (Note: Dabrafenib monotherapy within 14 days prior to starting combination therapy is allowed for crossover subjects in Cohort A); * Current use of a prohibited medication or expected to require any of these medications during treatment with study treatment. * Unresolved toxicity of National Cancer Institute Common Terminology Criteria for Adverse Events, version 4.0 (NCI CTCAE v4.0) Grade 2 or higher from previous anti-cancer therapy, except alopecia; * Presence of active gastrointestinal disease or other condition that will interfere significantly with the absorption of drugs. If clarification is needed as to whether a condition will significantly affect absorption of drugs, contact the GSK medical monitor for guidance to enrol the subject; * Known Hepatitis B Virus (HBV) or Hepatitis C Virus (HCV) infection. Subjects with laboratory evidence of cleared HBV and HCV infection may be enrolled; * History of another malignancy \< 3 years prior to starting study treatment or any malignancy with confirmed activating RAS-mutation; Exceptions: Subjects with any of the following malignancies within 3 years (does not include malignancies with confirmed activating RAS-mutation) are eligible: (a) a history of completely resected skin cancer, (b) successfully treated in situ carcinoma, (c) chronic lymphocytic lymphoma (CLL) in stable remission, or (d) indolent prostate cancer (definition: clinical stage T1 or T2a, Gleason score \<= 6, and prostate specific antigen \[PSA\] \< 10 ng/mL) requiring no or only anti-hormonal therapy with histologically confirmed tumour lesions that can be clearly differentiated from lung cancer target and non-target lesions are eligible * Subjects with brain metastases are excluded if their brain metastases are: * Symptomatic OR * Treated (surgery, radiation therapy) but not clinically and radiographically stable 3 weeks after local therapy(as assessed by contrast enhanced magnetic resonance imaging \[MRI\] or computed tomography \[CT\]), OR * Asymptomatic and untreated but \>1 cm in the longest dimension * A history or evidence of cardiovascular risk including any of the following: Corrected QT (QTc) interval \>=480 msecs History of acute coronary syndromes (including myocardial infarction or unstable angina) within 6 months prior to first dose of study treatment Coronary angioplasty, or stenting within the past 24 weeks; A history or evidence of current Class II, III, or IV heart failure as defined by the New York Heart Association (NYHA) guidelines; Treatment refractory hypertension defined as a blood pressure of systolic \>140 mmHg and/or diastolic \>90 mmHg which cannot be controlled by antihypertensive therapy; Abnormal cardiac valve morphology ( \>=Grade 2) documented by echocardiogram (subjects with Grade 1 abnormalities \[i.e., mild regurgitation/stenosis\] can be entered on study). Subjects with moderate valvular thickening should not be entered on study; Patients with intra-cardiac defibrillators A history or evidence of current clinically significant uncontrolled arrhythmias; Exception: Subjects with atrial fibrillation controlled for \> 30 days prior to randomization are eligible. Uncontrolled medical conditions (i.e., diabetes mellitus, hypertension, etc.), psychological, familial, sociological, or geographical conditions that interfere with the subject's safety or obtaining informed consent or do not permit compliance with the protocol; or unwillingness or inability to follow the procedures required in the protocol; * Pregnant, or actively breastfeeding females. * Known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to the study treatments, their excipients, and/or dimethyl sulfoxide (DMSO) * Additional Exclusion Criteria for dabrafenib and trametinib combination therapy (Cohort B and C as well as subjects that crossover from monotherapy to combination therapy): * History of interstitial lung disease or pneumonitis * A history or current evidence of retinal vein occlusion (RVO).