Inclusion Criteria:

          1. Histologically or cytologically confirmed recurrent non-small cell lung cancer not
             amendable to curative intent therapy or stage IV NSCLC.

          2. Known KRAS mutation status by CLIA certified test. Patients in the safety run-in are
             not required to have a tumor with mutant KRAS. In the randomized portion of the trial,
             only patients with KRAS mutation are eligible.

          3. Documented progression following at least one line of chemotherapy for metastatic or
             recurrent disease, or progression within 6 months of receiving adjuvant chemotherapy
             or concurrent chemotherapy for early stage or locally advanced disease.

          4. Biopsy accessible disease and willingness to undergo tumor biopsy.

          5. Measurable disease by RECIST 1.1.

          6. Age>/= 18 years.

          7. ECOG performance status 0 or 1.

          8. Ability to take pills by mouth.

          9. Patients must have normal organ and marrow function as defined: leukocytes
             >/=3,000/mcL, absolute neutrophil count >/=1,500/mcL, platelets >/=100,000/mcL,
             hemoglobin >/9.0g/dL, total bilirubin </=1.5 x upper limit of normal (ULN) (higher is
             allowed if in the setting of known Gilbert's disease), AST(SGOT)/ALT(SGPT) </=2.5 x
             institutional upper limit of normal or </=5 x ULN if liver metastases are present,
             Alkaline phosphatase </=3.5 x institutional upper limit of normal or <6 x ULN if liver
             metastases are present, creatinine clearance >/=50 mL/min/1.73^2 by Cockcroft-Gault
             equation (creatinine clearance= ([140-age]x body mass)/(plasma creatinine x 72) x
             gender correction factor) or by 24-hour urine collection.

         10. Brain metastases are allowed, as long as they are stable and do not require treatment
             with anticonvulsants or escalating doses of steroids.

         11. Females of childbearing potential must have a negative serum pregnancy test and must
             agree to use adequate contraception for the duration of the study and six months
             after. Females of childbearing potential are defined as those who are not surgically
             sterile (ie, bilateral tubal ligation, bilateral oophorectomy, or complete
             hysterectomy) or postmenopausal (defined as 12 months with no menses without an
             alternative medical cause). Continued in #12

         12. Continued from #11: a) Acceptable effective methods of contraception for women include
             implants, injectables, combined oral contraceptives, some intrauterine devices/systems
             and sterilization including vasectomy of the partner, all being used in combination
             with barrier methods of contraception (e.g. condoms). b) True sexual abstinence is
             also an acceptable method of contraception. Continued in #13

         13. Continued from #12: Women will be considered post-menopausal if they have been
             amenorrheic for the past 12 months without an alternative medical cause. The following
             age-specific requirements must also apply: i.)Women < 50 years old: they would be
             considered post-menopausal if they have been amenorrheic for the past 12 months or
             more following cessation of exogenous hormonal treatments. The levels of Luteinizing
             Hormone (LH) and Follicle-Stimulating Hormone (FSH) must also be in the
             post-menopausal range (as per the institution). ii.)Women >/= 50 years old: they would
             be consider post-menopausal if they have been amenorrheic for the past 12 months or
             more following cessation of all exogenous hormonal treatments, or have had
             radiation-induced oophorectomy with the last menses > 1 year ago, or have had
             chemotherapy-induced menopause with >1 year interval since last menses, or have had
             surgical sterilisation by either bilateral oophorectomy or hysterectomy.

         14. Non-sterilized males who are sexually active with a female partner of childbearing
             potential must use adequate contraception for the duration of the study and 90 days
             after the last dose of study medication. a) Acceptable methods of contraception for
             men include the use of condoms with spermicidal foams/gels or prior vasectomy. b) True
             sexual abstinence is also an acceptable method of contraception.

         15. Ability to understand and the willingness to sign a written informed consent document.

         16. Have adequate renal function, with a GFR of >/= 50ml/min by the Cockcroft-Gault
             formula or by 24 hour urine collection.

        Exclusion Criteria:

          1. Have received or are receiving an investigational medicinal product (IMP) or other
             systemic anticancer treatment within 4 weeks prior to the first dose of study
             treatment, or within a period during which the IMP or systemic anticancer treatment
             has not been cleared from the body (e.g. a period of 5 'half-lives'), whichever is the
             most appropriate and as judged by the investigator.

          2. Current or prior use of immunosuppressive medication within 14 days of the 1st dose of
             durvalumab, 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.

          3. Any concurrent chemotherapy, immunotherapy, biologic, or hormonal therapy for cancer
             treatment.

          4. Receipt of radiation therapy within 4 weeks prior to starting study treatment. Limited
             field of radiation for palliation at any time prior to the start of study treatment is
             acceptable if: i.) The lung is not in the radiation field ii.) The irradiated lesions
             are not used as target lesions.

          5. Receipt of live attenuated vaccination within 30 days prior to study entry or within
             30 days of receiving durvalumab.

          6. Prior treatment with a MEK, Ras, or Raf inhibitor, or CTLA4 inhibitor.

          7. Patients who are receiving any other investigational agents.

          8. Have any unresolved chronic toxicity with CTCAE grade >/= 2, from previous anticancer
             therapy, except for alopecia.

          9. Known hypersensitivity to selumetinib or durvalumab or any excipient or history of
             allergic reactions attributed to compounds of similar chemical or biologic composition
             to selumetinib or durvalumab.

         10. Active or prior documented autoimmune disease within the past 3 years. Patients with a
             history of vitiligo, Grave's disease, or psoriasis not requiring systemic treatment
             (within the past 2 years) are not excluded.

         11. Active or prior documented inflammatory bowel disease (e.g. Crohn's disease,
             ulcerative colitis).

         12. Have known or suspected brain metastases or spinal cord compression, unless the
             condition has been asymptomatic, has been treated with surgery and / or radiation, and
             has been stable without requiring corticosteroids nor anti-convulsant medications for
             at least 4 weeks prior to the first dose of study medication.

         13. Known history of previous clinical diagnosis of tuberculosis.

         14. History of primary immunodeficiency.

         15. History of organ transplant requiring therapeutic immunosuppression.

         16. Cardiac conditions as follows: i.) Mean QT interval corrected for heart rate (QTc)
             >/=450 ms calculated from 3 ECGs using Fredericia's formula [QTcF] or other factors
             that increase the risk of QT prolongation. ii.) Uncontrolled hypertension (BP >/=
             150/95 despite optimal medical therapy). iii.) Acute coronary syndrome within 6 months
             prior to starting treatment. iv.) Uncontrolled Angina - Canadian Cardiovascular
             Society grade II-IV despite medical therapy. v.) Symptomatic heart failure NYHA Class
             II-IV, prior or current cardiomyopathy, or severe valvular heart disease. - Criteria
             continued in #17

         17. Continued from #16: vi.) Prior or current cardiomyopathy including but not limited to
             the following: a) known hypertrophic cardiomyopathy b) known arrhythmogenic right
             ventricular cardiomyopathy c) previous moderate or severe impairment of left
             ventricular systolic function (LVEF <45% on echocardiography or equivalent on MuGA)
             even if full recovery has occurred. vii.) Baseline Left ventricular ejection fraction
             (LVEF) below the LLN or <55% measured by echocardiography or institution's LLN for
             MUGA. viii.) Severe valvular heart disease. ix.) Atrial fibrillation with a
             ventricular rate > 100 bpm on ECG at rest.

         18. Ophthalmologic conditions as follows: i.) Current or past history of retinal pigment
             epithelial detachment (RPED)/central serous retinopathy (CSR) or retinal vein
             occlusion. ii.) Intraocular pressure (IOP) > 21 mmHg or uncontrolled glaucoma
             (irrespective of IOP).

         19. Any gastrointestinal disorder expected to limit absorption of selumetinib

         20. History of another primary malignancy within 5 years prior to starting study
             treatment, except for adequately treated basal or squamous cell carcinoma of the skin
             or cancer of the cervix in situ

         21. Recent major surgery within 4 weeks prior to starting study treatment, with the
             exception of surgical placement for vascular access.

         22. Uncontrolled intercurrent illness including, but not limited to, uncompensated
             respiratory, cardiac, hepatic, or renal disease, active infection (including hepatitis
             B, hepatitis C, HIV, and active clinical tuberculosis), active bleeding diatheses or
             renal transplant; ongoing or active infection, symptomatic congestive heart failure,
             unstable angina pectoris, cardiac arrhythmia, active peptic ulcer disease or
             gastritis, or psychiatric illness/social situations that would limit compliance with
             study requirements.

         23. Pregnant or breastfeeding women.

         24. Receiving or have received systemic anti-cancer therapy within 4 weeks prior to
             starting study treatment (6 weeks for nitrosoureas, mitomycin, and suramin), or any
             anticancer therapy which has not been cleared from the body by the time of starting
             study treatment.

         25. Have evidence of any other significant clinical disorder or laboratory finding that,
             as judged by the investigator, makes it undesirable for the patient to participate in
             the study.

         26. Have refractory nausea and vomiting, chronic gastrointestinal diseases (e.g.,
             inflammatory bowel disease), or significant bowel resection that would adversely
             affect the absorption / bioavailability of the orally administered study medication.

         27. Are male or female patients of reproductive potential and, as judged by the
             investigator, are not employing an effective method of birth control.

         28. Patient weight less than 30 kg.