Study of Selumetinib in Patients With Previously Treated or Untreated Advanced/Metastatic NSCLC

Inclusion Criteria: * Histologically and/or cytologically confirmed NSCLC that is metastatic or unresectable and for which standard curative measures do not exist. * All patients must have a formalin fixed paraffin embedded tissue block (from primary or metastatic tumour) available for correlative studies and must have provided informed consent for the release of the block as well as for blood samples for correlative studies. * Although KRAS mutation is not mandatory, patients accrued to the RP2D expansion cohorts will have a sample sent for KRAS screening; patients must also have at least one site of disease which is unidimensionally measurable. * Measurable disease defined as at least one target lesion that has not been irradiated and can be accurately measured in at least one dimension by RECIST 1.1 criteria. * Chest X-ray ≥ 20 mm * CT/MRI scan (with slice thickness of \< 5 mm) ≥ 10 mm --\> longest diameter * Physical exam (using calipers) ≥ 10 mm * Lymph nodes by CT scan ≥ 15 mm --\> measured in short axis * Presence of clinically and/or radiologically documented disease (marker positive only patients are not eligible). All radiology studies must be performed within 28 days prior to registration (within 35 days if negative). * Age \> 18 years. * ECOG performance status 0 or 1 * Patients must have a life expectancy of at least 12 weeks. Previous Therapy Surgery: Previous major surgery is permitted provided it has been at least 14 days prior to patient registration and that wound healing has occurred. Radiation: Prior external beam radiation is permitted provided a minimum of 4 weeks has elapsed between the last dose and enrollment to the trial. Chemotherapy and systemic therapy: Patients may not have received prior MEK inhibitors or any other tyrosine kinase inhibitor (including EGFR inhibitors of any kind). Prior adjuvant chemotherapy or combined chemoradiotherapy with curative intent is permissible provided completed at least one year prior to enrollment. No prior cytotoxic chemotherapy for advanced / metastatic disease is permissible, UNLESS patient is to be enrolled in the pemetrexed single agent cohort. Patients for this cohort must be candidates for single agent pemetrexed, have received no prior pemetrexed and have had no more than one prior chemotherapy regimen for advanced or metastatic disease. Laboratory Requirements (must be done within 7 days prior to registration) Hematology: Neutrophils ≥ 1.5 x 10\^9/L; Platelets ≥ 100 x 10\^9/L Biochemistry: Creatinine Clearance\* ≥ 50 ml/min (calculated by Cockcroft and Gault equation) Total bilirubin ≤ 1.5 x ULN AST and ALT ≤ 2.5 x ULN (≤ 5x ULN in the presence of liver metastases) * Patient consent must be appropriately obtained in accordance with applicable local and regulatory requirements. Each patient must sign a consent form prior to enrollment in the trial to document their willingness to participate.Patients who cannot give informed consent (i.e. mentally incompetent patients, or those physically incapacitated such as comatose patients) are not to be recruited into the study. Patients competent but physically unable to sign the consent form may have the document signed by their nearest relative or legal guardian. Each patient will be provided with a full explanation of the study before consent is requested. * Patients must be accessible for treatment and follow-up. Patients registered on this trial must be treated and followed at the participating centre. This implies there must be reasonable geographical limits (for example: 1 ½ hour's driving distance) placed on patients being considered for this trial. Investigators must assure themselves the patients registered on this trial will be available for complete documentation of the treatment, adverse events, and follow-up. * Treatment is to begin within 2 working days of patient registration. Exclusion Criteria: * Patients of Asian ethnicity are not eligible for the dose escalation phase of the study. Asian patients may be enrolled in the RP2D following informed consent and at the investigators discretion. * Patients with a history of other untreated malignancies or malignancies which required therapy within the past 2 years. * Patients with documented brain metastasis or carcinomatous meningitis, treated or untreated. * Patients with significant cardiac disease, including: * any factors that increase the risk of QTc prolongation or risk of arrhythmic events (e.g. heart failure, hypokalaemia, congenital long QT syndrome, family history of long QT syndrome or unexplained sudden death under 40 years of age) or mean resting corrected QT interval (QTc) \> 470 msec * uncontrolled hypertension (BP ≥ 150/95 mmHg despite medical therapy) * acute coronary syndrome within 6 months prior to starting treatment * angina Canadian Cardiovascular Society Grade II-IV (despite medical therapy) * symptomatic heart failure (NYHA II-IV) * prior or current cardiomyopathy * atrial fibrillation with a ventricular rate \> 100bpm at rest * severe valvular heart disease * Other patients with cardiac disease, who do not meet the exclusion criteria above, must have a baseline LVEF ≥ 55%. * Patients who have neuropathy \> grade 1 or other conditions precluding treatment with the standard chemotherapy regimen planned. * Patients who have significant gastrointestinal disease and who are unable to swallow capsules. * Patients on potent inhibitors or inducers of CYP3A4/5, CYP2C19 and CYP1A2 (must have discontinued within 2 weeks prior to registration (3 weeks for St. John's Wort). Patients who do not agree to avoid the ingestion of large amounts of grapefruit and Seville oranges (and other products containing these fruits, e.g. grapefruit juice or marmalade). Participants who are taking supplemental vitamin E, that cannot be discontinued, are not eligible for the study. Patients who require oral anticoagulants (coumadin) are eligible provided there is increased vigilance with respect to monitor INR, upon initiation of dosing with selumetinib. If medically appropriate and treatment available, the investigator should consider switching these patients to LMW heparin. * Patients with current or past history of central serous retinopathy or retinal vein occlusion, high intraocular pressure or uncontrolled glaucoma (irrespective of IOP). * Pregnant or lactating women. Women of childbearing potential must have a urine pregnancy test proven negative within 7 days prior to registration. Men and women of child-bearing potential must agree to use adequate contraception. * Patients who do not agree to avoid excessive sun exposure and use adequate sunscreen protection.