Inclusion Criteria:

          -  Patients must have histologically or cytologically confirmed stage IV non-squamous
             non-small cell lung cancer (NSCLC) (includes M1a, M1b, and M1c stage disease, American
             Joint Committee on Cancer [AJCC] 8th edition). Patients with Stage IIIB and IIIC
             disease are eligible if they are not candidates for combined chemotherapy and
             radiation

          -  Patients must have PD-L1 expression Tumor Proportion Score (TPS) >= 1% in tumor cells.
             If PD-L1 expression TPS is unevaluable or the testing could not be completed, the
             patients are not eligible. The assay must have been performed by a Clinical Laboratory
             Improvement Act (CLIA) (or equivalent) certified laboratory

          -  Patients must have measurable or non-measurable disease. The presence of malignant
             pleural fluid alone is sufficient to satisfy this eligibility criterion. Baseline
             imaging assessments and measurements used to evaluate all measurable or non-measurable
             sites of disease must be done within 4 weeks prior to study registration

               -  NOTE: If patient receives pemetrexed, follow institutional guidelines to drain
                  fluids

          -  Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of
             0 to 1

          -  Patients must NOT have received the following:

               -  Prior systemic chemotherapy or immunotherapy for advanced metastatic NSCLC.
                  Patients treated with any prior checkpoint inhibitors for metastatic lung cancer
                  are ineligible. Chemotherapy for non-metastatic disease (e.g. adjuvant therapy)
                  or immunotherapy for locally advanced Stage III disease is allowed if at least 6
                  months have elapsed between the last dose of the prior therapy and study
                  registration. Local therapy, e.g. palliative radiation, is allowed as long as a
                  period of 14 days has passed between completion of local therapy and study
                  registration. Registration prior to treatment during the 14 days is allowed.
                  Palliative radiation must be to non-target lesions

               -  Methotrexate (MTX) given in low doses for non-malignant conditions with last dose
                  at least 14 days prior to date of registration will be allowed. Other low dose
                  chemotherapeutics for non-malignant conditions will be considered, but review by
                  the study chair is required

          -  Patients with known EGFR mutations (except exon 20 insertion), BRAF mutations (V600)
             or ALK or ROS1 translocations that can be treated with oral tyrosine kinase inhibitors
             are excluded

          -  Patients with treated brain metastases are eligible if follow-up brain imaging after
             central nervous system (CNS)-directed therapy shows no evidence of progression. CNS
             progression counts as progression and patients must move on to the next phase after
             CNS treatment. Patients with asymptomatic new (at screening) or progressive brain
             metastases (active brain metastases at screening) or leptomeningeal disease are
             eligible if the treating physician determines that immediate CNS specific treatment is
             not required and is unlikely to be required during the first cycle of therapy

               -  Patients are eligible if off steroids for at least 14 days prior to protocol
                  treatment

               -  Palliative radiation to non-target lesions (bone metastasis) is allowed if
                  patient develops symptoms

               -  Anticonvulsants are allowed

               -  Patients with asymptomatic, sub-centimeter brain metastasis who at the discretion
                  of investigators do not need immediate CNS directed therapies are eligible

          -  Patients with prior or concurrent malignancy whose natural history or treatment does
             not have the potential to interfere with the safety or efficacy assessment of the
             investigational regimen are eligible for this trial

          -  Patients must not have known pre-existing and clinically active interstitial lung
             disease, or a known history of (non infectious) pneumonitis that required steroids, or
             current pneumonitis

          -  Patients must not have significant gastrointestinal disorders with diarrhea as a major
             symptom (e.g. Crohn's disease, malabsorption, etc.)

          -  Patients must not have history of auto-immune condition requiring ongoing or
             intermittent systemic treatment in the past 2 years (i.e. with use of disease
             modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy
             (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for
             adrenal or pituitary insufficiency, etc.) is not considered a form of systemic
             treatment

          -  Patients with known history or current symptoms of cardiac disease, or history of
             treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac
             function using the New York Heart Association Functional Classification. To be
             eligible for this trial, patients should be class 2B or better

          -  Patients must not have any other concomitant serious illness or organ system
             dysfunction that in the opinion of the investigator would either compromise patient
             safety or interfere with the evaluation of the safety of the study drug

          -  Patients must not receive any other investigational agents during the course of
             therapy

          -  Women must not be pregnant or breast-feeding due to potential harm to the fetus or
             infant from cytotoxic chemotherapy and the unknown risk of MK-3475 (pembrolizumab).
             Patients must also not expect to conceive or father children from the time of
             registration, while on study treatment, and until at least 120 days after the last
             dose of study treatment

               -  All females of childbearing potential must have a blood test or urine study
                  within 72 hours prior to registration to rule out pregnancy

               -  A female of childbearing potential is any woman, regardless of sexual orientation
                  or whether they have undergone tubal ligation, who meets the following criteria:
                  has achieved menarche at some point; has not undergone a hysterectomy or
                  bilateral oophorectomy; or has not been naturally postmenopausal (amenorrhea
                  following cancer therapy does not rule out childbearing potential) for at least
                  24 consecutive months (i.e., has had menses at any time in the preceding 24
                  consecutive months)

          -  Women of childbearing potential and sexually active males must use an accepted and
             effective method of contraception or abstain from sexual intercourse from time of
             registration, while on study treatment, and continue for 120 days after the last dose
             of study treatment

          -  Absolute neutrophil count (ANC) >= 1500/mm^3 (within 14 days of randomization)

          -  Platelets >= 100,000/mm^3 (within 14 days of randomization)

          -  Prothrombin time (PT)/international normalized ratio (INR) =< 1.5 Or if patient on
             therapeutic anticoagulation, PT/INR =< 3.0 (within 14 days of randomization)

          -  Partial thromboplastin time (PTT) =< institutional upper limit of normal (ULN) OR, if
             patient is on therapeutic anticoagulation, PTT must be =< 1.5 x ULN (within 14 days of
             randomization)

          -  Total bilirubin =< 1.5 mg/dL (obtained within 14 days of randomization)

          -  Serum glutamic-oxaloacetic transaminase (SGOT) (aspartate aminotransferase [AST]) < 5
             x upper limit of normal (ULN) (obtained within 14 days of randomization)

          -  Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase [ALT]) < 5 x
             upper limit of normal (ULN) (obtained within 14 days of randomization)

          -  Calculated creatinine clearance >= 45 ml/min to be eligible to receive pemetrexed
             (obtained within 14 days prior to randomization)

          -  Serum creatinine =< 1.5 x institutional upper limit of normal (ULN) (obtained within
             14 days prior to randomization)

          -  Patients must not have a known history of active tuberculosis (TB)

          -  Patients must not have a diagnosis of immunodeficiency or receive systemic steroid
             therapy or any other form of immunosuppressive therapy within 7 days prior to the
             first dose of protocol treatment

          -  Patients must not have received a live vaccine within 30 days prior to randomization.
             Seasonal flu vaccines that do not contain live virus are permitted

          -  Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral
             therapy with undetectable viral load within 6 months are eligible for this trial

          -  For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral
             load must be undetectable or on suppressive therapy, if indicated. Patients with a
             history of hepatitis C virus (HCV) infection must have been treated and cured. For
             patients with HCV infection who are currently on treatment, they are eligible if they
             have an undetectable HCV viral load