Inclusion Criteria:

          -  Written informed consent and any locally-required authorization will be obtained from
             the patient prior to performing any protocol-related procedures, including screening
             evaluations

          -  Patient is willing and able to comply with the protocol for the duration of the study
             including undergoing treatment and scheduled visits and examinations including follow
             up

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

          -  Known KRAS mutation status by Clinical Laboratory Improvement Act (CLIA) certified
             test

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

          -  Biopsy accessible disease and willingness to undergo tumor biopsy

          -  Measurable disease by RECIST 1.1

          -  Total body weight > 30 kg

          -  Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1

          -  Ability to take pills by mouth

          -  Leukocytes >= 3,000/mcL

          -  Absolute neutrophil count >= 1,500/mcL

          -  Platelets >= 100,000/mcL

          -  Hemoglobin >= 9.0 g/dL

          -  Total bilirubin total bilirubin =<1.5 x upper limit of normal (ULN) (higher is allowed
             if in the setting of known Gilbert's disease)

          -  Aspartate aminotransferase (AST)(serum glutamic-oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT)(serum glutamate pyruvate transaminase [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 m2 by Cockcroft-Gault equation or by 24-hour
             urine collection

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

          -  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

          -  Have adequate renal function, with a glomerular filtration rate (GFR) of >= 50 ml/min
             by the Cockcroft-Gault formula or by 24 hour urine collection

        Exclusion Criteria:

          -  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

          -  Concurrent enrollment in another clinical study, unless it is an observational
             (non-interventional) clinical study or during the follow-up period of an
             interventional study

          -  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

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

          -  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: a) the lung is not in the radiation field, b) the irradiated lesions
             are not used as target lesions

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

          -  Prior treatment with a MEK, Ras, or Raf inhibitor

          -  Patients who have received prior anti PD-1, anti PD-L1 or anti CTLA-4 a) must not have
             experienced a toxicity that led to permanent discontinuation of prior immunotherapy.
             b) all adverse events (AEs) while receiving prior immunotherapy must have completely
             resolved or resolved to baseline prior to screening for this study c) must not have
             experienced a >= grade 3 immune related AE or an immune related neurologic or ocular
             AE of any grade while receiving prior immunotherapy. NOTE: Patients with endocrine AE
             of =< grade 2 are permitted to enroll if they are stably maintained on appropriate
             replacement therapy and are asymptomatic

          -  Must not have required the use of additional immunosuppression other than
             corticosteroids for the management of an AE, not have experienced recurrence of an AE
             if re-challenged, and not currently require maintenance doses of > 10 mg prednisone or
             equivalent per day

          -  Patients who are receiving any other investigational agents

          -  Any unresolved chronic toxicity with Common Toxicity Criteria (CTC) AE grade >= 2,
             from previous anticancer therapy, except for alopecia. Any unresolved toxicity
             National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE)
             grade >= 2 from previous anticancer therapy with the exception of alopecia, vitiligo,
             and the laboratory values defined in the inclusion criteria. 1) Patients with grade >=
             2 neuropathy will be evaluated on a case-by-case basis after consultation with the
             study physician. 2) Patients with irreversible toxicity not reasonably expected to be
             exacerbated by treatment with durvalumab or tremelimumab may be included only after
             consultation with the study physician

          -  Known hypersensitivity to selumetinib, durvalumab, tremelimumab or any excipient or
             history of allergic reactions attributed to compounds of similar chemical or biologic
             composition to selumetinib, tremelimumab or durvalumab

          -  Active or prior documented autoimmune or inflammatory disorders (including
             inflammatory bowel disease (e.g., colitis or Crohn's disease), diverticulitis (with
             the exception of diverticulosis), systemic lupus erythematosus, Sarcoidosis syndrome,
             or Wegener syndrome (granulomatosis with polyangiitis, Graves' disease, rheumatoid
             arthritis, hypophysitis, uveitis, etc). The following are exceptions to this
             criterion: a) patients with vitiligo or alopecia, b) patients with hypothyroidism
             (e.g., following Hashimoto syndrome) stable on hormone replacement, c) any chronic
             skin condition that does not require systemic therapy, d) patients without active
             disease in the last 5 years may be included but only after consultation with the study
             physician, e) patients with celiac disease controlled by diet alone

          -  Active infection including tuberculosis (clinical evaluation that includes clinical
             history, physical examination and radiographic findings, and tuberculosis [TB] testing
             in line with local practice), hepatitis B (known positive hepatitis B virus [HBV]
             surface antigen [HBsAg] result), hepatitis C, or human immunodeficiency virus
             (positive HIV 1/2 antibodies). Patients with a past or resolved HBV infection (defined
             as the presence of hepatitis B core antibody [anti-HBc] and absence of HBsAg) are
             eligible. Patients positive for hepatitis C (HCV) antibody are eligible only if
             polymerase chain reaction is negative for HCV ribonucleic acid (RNA)

          -  History of leptomeningeal carcinomatosis

          -  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

          -  Known history of previous clinical diagnosis of tuberculosis

          -  History of primary immunodeficiency

          -  History of organ transplant requiring therapeutic immunosuppression

          -  Cardiac conditions as follows: a) mean QT interval corrected for heart rate (QTc) 450
             ms calculated from 3 electrocardiogram (ECGs) using Fredericia's formula (QTcF) or
             other factors that increase the risk of QT prolongation, b) uncontrolled hypertension
             (blood pressure [BP] 150/95 despite optimal medical therapy), c) acute coronary
             syndrome within 6 months prior to starting treatment d) uncontrolled angina - Canadian
             Cardiovascular Society grade II-IV despite medical therapy, e) symptomatic heart
             failure New York Heart Association (NYHA) class II-IV, prior or current
             cardiomyopathy, or severe valvular heart disease, f) prior or current cardiomyopathy
             including but not limited to the following: i) known hypertrophic cardiomyopathy, ii)
             known arrhythmogenic right ventricular cardiomyopathy, iii) previous moderate or
             severe impairment of left ventricular systolic function (LVEF < 45% on
             echocardiography or equivalent on multi-gated acquisition scan [MuGA]) even if full
             recovery has occurred, g) baseline left ventricular ejection fraction (LVEF) below the
             lower limit of normal (LLN) or < 55% measured by echocardiography or institution's LLN
             for MUGA, h) severe valvular heart disease, i) atrial fibrillation with a ventricular
             rate > 100 beats per minute (bpm) on ECG at rest

          -  Ophthalmologic conditions as follows: a) current or past history of retinal pigment
             epithelial detachment (RPED)/central serous retinopathy (CSR) or retinal vein
             occlusion, b) intraocular pressure (IOP) > 21 mmHg or uncontrolled glaucoma
             (irrespective of IOP)

          -  Any gastrointestinal disorder expected to limit absorption of selumetinib

          -  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

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

          -  Uncontrolled intercurrent illness, including but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable
             angina pectoris, cardiac arrhythmia, interstitial lung disease, serious chronic
             gastrointestinal conditions associated with diarrhea, or psychiatric illness/social
             situations that would limit compliance with study requirement, substantially increase
             risk of incurring AEs or compromise the ability of the patient to give written
             informed consent

          -  Pregnant or breastfeeding women

          -  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

          -  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

          -  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

          -  Are male or female patients of reproductive potential and, as judged by the
             investigator, are not employing an effective method of birth control from screening to
             180 days after the last dose of durvalumab and tremelimumab combination therapy

          -  Patient weight =< 30 kg