This phase I/II trial studies the best dose of selumetinib and how well it works with durvalumab and tremelimumab in treating participants with stage IV non-small cell lung cancer or that has come back. Immunotherapy with monoclonal antibodies, such as durvalumab and tremelimumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Selumetinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Giving durvalumab, tremelimumab and selumetinib may work better in treating participants with non-small lung cancer.

PRIMARY OBJECTIVES:

I. To determine the maximum tolerated dose (MTD). (Dose-escalation phase) II. To estimate the progression free survival in patients with previously treated non-small cell lung cancer (NSCLC) treated with durvalumab and tremelimumab in combination with selumetinib in either an intermittent or continuous schedule and compare to historical controls. (Dose expansion phase)

SECONDARY OBJECTIVES:

I. To assess response rate by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1.

II. To assess disease control rate (complete response + partial response + stable disease).

III. To assess overall survival. IV. To assess safety and toxicity (in the dose-escalation and dose expansion phases).

V. To assess duration of response.

EXPLORATORY OBJECTIVES:

I. To assess markers of response and resistance in pre-treatment and on- treatment biopsies.

OUTLINE: This is a phase I, dose-escalation study of selumetinib followed by a phase II study. Participants are randomized to 1 of 2 arms.

ARM I: Participants receive selumetinib orally (PO) twice daily (BID) on days 1-7 and 15-21 and durvalumab intravenously (IV) over 60 minutes on day 1. Participants also receive tremelimumab IV over 60 minutes on day 1 for courses 1-4. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity.

ARM II: Participants receive selumetinib PO BID on days 1-28 and durvalumab IV over 60 minutes on day 1. Participants also receive tremelimumab IV over 60 minutes on day 1 for courses 1-4. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, participants are followed up at 30 and 90 days, then every 6 months for up to 2 years.

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