Inclusion Criteria:

          -  Ability to understand the purpose and risks of the study and provide signed and dated
             informed consent and authorization to use protected health information (PHI)

          -  Have a life expectancy of at least 3 months

          -  Have a histologically or cytologically confirmed diagnosis of non-small cell lung
             cancer (NSCLC) and have at least one measurable lesion as defined by modified Response
             Evaluation Criteria in Solid Tumors (RECIST) 1.1; the target lesion(s) should also
             have bi-dimensional measurability for RECIST 1.1 evaluation on study

          -  Have an EGFR mutation (sensitizing or non-sensitizing)

          -  Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG)
             performance scale

          -  Absolute neutrophil count (ANC) >= 1,500 /microliters(mcL)

          -  Platelets >= 100,000 / mcL

          -  Hemoglobin >= 9 g/dL or >= 5.6 mmol/L without transfusion or erythropoietin (EPO)
             dependency (within 7 days of assessment)

          -  Serum creatinine =< 1.5 X upper limit of normal (ULN) OR measured or calculated
             creatinine clearance (glomerular filtration rate [GFR] can also be used in place of
             creatinine or creatinine clearance (CrCl)) >= 60 mL/min for subject with creatinine
             levels > 1.5 x institutional ULN

          -  Serum total bilirubin =< 1.5 x ULN OR direct bilirubin =< ULN for subjects with total
             bilirubin levels > 1.5 ULN

          -  Aspartate transaminase (AST) (serum glutamic oxaloacetic transaminase (SGOT)) and
             alanine transferase (ALT) (serum glutamate pyruvate transaminase (SGPT)) =< 2.5 X ULN
             OR =< 5 X ULN for subjects with liver metastases

          -  Albumin >= 2.5 mg/dL

          -  International Normalized Ratio (INR) or Prothrombin Time (PT) =< 1.5 X ULN unless
             subject is receiving anticoagulant therapy as long as PT or partial thromboplastin
             time (PTT) is within therapeutic range of intended use of anticoagulants

          -  Activated partial thromboplastin time (aPTT) =< 1.5 X ULN unless subject is receiving
             anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use
             of anticoagulants

          -  Have provided tissue for PD-L1 biomarker analysis from a newly obtained formalin fixed
             tumor tissue from a biopsy of a tumor lesion not previously irradiated; the tissue
             sample must be received and evaluated by the study site prior to start of treatment;
             fine needle aspirates are not acceptable; needle or excisional biopsies, or resected
             tissue is required

          -  Have a PD-L1 positive (either strongly or weakly) tumor as determined by the IHC 22C3
             pharmDx test at the study site; if a patient's initial tumor specimen is not
             classified as PD-L1 positive by the central laboratory, a newly obtained specimen
             (different from the sample previously submitted) may be submitted for testing; if the
             newer specimen is classified as PD-L1 positive by the study site, the patient meets
             this eligibility criterion

          -  Have resolution of toxic effect(s) of the most recent prior chemotherapy to grade 1 or
             less (except alopecia); if subject received major surgery or radiation therapy of > 30
             Gy, they must have recovered from the toxicity and/or complications from the
             intervention

          -  Female subject of childbearing potential has a negative urine or serum pregnancy test;
             if the urine test is positive or cannot be confirmed as negative, a serum pregnancy
             test will be required; the serum pregnancy test must be negative for the subject to be
             eligible

          -  Female subjects may be enrolled in the trial if they are:

               -  of non-childbearing potential which is defined as:

               -  of childbearing potential who are willing to use either 2 adequate barrier
                  methods or a barrier method plus a hormonal method of contraception to prevent
                  pregnancy, or to abstain from heterosexual activity throughout the trial,
                  starting with the screening visit (visit 1) through 120 days after the last dose
                  of MK-3475 (pembrolizumab)

          -  Male subjects should agree to use an adequate method of contraception starting with
             the first dose of study therapy through 120 days after the last dose of study therapy

        Exclusion Criteria:

          -  Has received prior therapy with an EGFR tyrosine kinase inhibitor (such as erlotinib,
             gefitinib, afatinib, rociletinib, or AZD9291) for NSCLC

          -  Is currently participating or has participated in a study of an investigational agent
             or using an investigational device within 30 days of the first dose of trial
             treatment; the 30 day window should be applied to the last dose of an antineoplastic
             investigational agent or last use of an investigational device with antineoplastic
             intent

          -  Is receiving systemic steroid therapy within three days prior to the first dose of
             trial treatment or receiving any other form of immunosuppressive medication
             (corticosteroid use on study for management of early combined immunosuppression (ECIs)
             is allowed)

          -  Is expected to require any other form of systemic or localized antineoplastic therapy
             while on trial (including maintenance therapy with another agent for NSCLC or
             radiation therapy)

          -  Has received prior systemic cytotoxic chemotherapy, antineoplastic biological therapy
             (e.g., cetuximab), major surgery within 3 weeks of the first dose of trial treatment;
             received thoracic radiation therapy of > 30 Gy within 6 months of the first dose of
             trial treatment

          -  Has received prior therapy with an anti-programmed cell death protein 1 (PD-1),
             anti-PD-L1, anti-programmed cell death 1 ligand 2 (PD-L2), anti-cluster of
             differentiation 137 (CD137), or anti-cytotoxic t-lymphocyte-associated antigen-4
             (CTLA-4) antibody (including ipilimumab or any other antibody or drug specifically
             targeting T-cell co-stimulation or checkpoint pathways); has participated in another
             MK-3475 clinical trial

          -  Has a known history of prior malignancy except if the patient has undergone
             potentially curative therapy with no evidence of that disease recurrence for 3 years
             since initiation of that therapy; Note: the time requirement for no evidence of
             disease for 3 years does not apply to the NSCLC tumor for which a subject is enrolled
             in this trial; the time requirement also does not apply to subjects who underwent
             successful definitive resection of basal cell carcinoma of the skin, superficial
             bladder cancer, squamous cell carcinoma of the skin, or in situ cervical cancer

          -  Has known active central nervous system (CNS) metastases and/or carcinomatous
             meningitis; subjects with previously treated brain metastases may participate provided
             they are stable (without evidence of progression by magnetic resonance imaging [MRI]
             for at least two weeks prior to the first dose of trial treatment and any neurologic
             symptoms have returned to baseline), have no evidence of new or enlarging brain
             metastases, and are using no steroids for at least three days prior to study
             medication

          -  Has an active autoimmune disease, or a documented history of autoimmune disease that
             required systemic steroids or immunosuppressive agents; subjects with vitiligo or
             resolved childhood asthma/atopy would be exception to this rule; subjects that require
             inhaled steroid or local steroid injections will not be excluded from the study;
             subjects with hypothyroidism not from autoimmune disease and stable on hormone
             replacement will not be excluded from the study

          -  Has had an allogeneic tissue/solid organ transplant

          -  Has interstitial lung disease or a history of pneumonitis that required oral or
             intravenous glucocorticoids to assist with management; lymphangitic spread of the
             NSCLC is not exclusionary

          -  Has received or will receive a live vaccine within 30 days prior to the first
             administration of study medication; seasonal flu vaccines that do not contain live
             virus are permitted

          -  Has an active infection requiring intravenous systemic therapy

          -  Has known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies)

          -  Has known active hepatitis B or C; active hepatitis B is defined as a known positive
             hepatitis B surface antigen (HBsAg) result; active hepatitis C is defined by a known
             positive hepatitis (Hep) C antibody (Ab) result and known quantitative hepatitis C
             virus (HCV) ribonucleic acid (RNA) results greater than the lower limits of detection
             of the assay

          -  Has a history or current evidence of any condition, therapy, or laboratory abnormality
             that might confound the results of the trial, interfere with the subject's
             participation for the full duration of the trial, or is not in the best interest of
             the subject to participate, in the opinion of the treating investigator

          -  Has known psychiatric or substance abuse disorders that would interfere with
             cooperation with the requirements of the trial

          -  Is, at the time of signing informed consent, a regular user (including "recreational
             use") of any illicit drugs or had a recent history (within the last year) of substance
             abuse (including alcohol)

          -  Is pregnant or breastfeeding, or expecting to conceive or father children within the
             projected duration of the trial, starting with the screening visit (visit 1) through
             120 days after the last dose of MK-3475