Effect of Pembrolizumab With or Without Carboplatin and Paclitaxel on Immune Response in Patients With Recurrent or Stage IIIB-IV Non-small Cell Lung Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed non-small cell lung cancer (NSCLC) that is advanced/metastatic (stage IIIB/IV) or recurrent (progression after surgery or radiation or chemo-radiation treatment for loco-regional disease). Patients with epidermal growth factor (EGFR) mutation, anaplastic lymphoma kinase (ALK) gene rearrangement or ROS1 translocation must have received an approved EGFR, ALK, or ROS1-directed therapy and have signs of disease progression prior to receiving pembrolizumab. * Patients must be willing to provide tissue from a newly obtained core or excisional biopsy of a tumor lesion; newly-obtained is defined as a specimen obtained up to 12 weeks (84 days) prior to date of signing consent. * Subjects for whom newly-obtained samples cannot be provided (e.g. inaccessible or subject safety concern) may submit an archived specimen (up to 3 years) only upon agreement from the Sponsor. At least 4 mm of tumor tissue will be needed for PD-L1 staining. * Patients who have received zero (0) to two (2) previous lines of systemic chemotherapy and are not currently receiving chemotherapy treatment (within 2 weeks of randomization). * At least one measurable lesion as defined by RECIST v1.1 on screening computed tomography (CT) or magnetic resonance imaging (MRI) * Age \>18 years. * ECOG performance status of 2. * Patients must have normal organ and marrow function as defined below: * white blood cell count \> 2,500 cells/mcL * absolute neutrophil count \>1,500/mcL * platelets \>100,000/mcL * hemoglobin ≥ 9 g/dL * total bilirubin ≤ 2.0 x upper limit of normal (ULN) * AST(SGOT)/ALT(SGPT) \< 2.5 x ULN Or ≤ 5 x ULN in presence of liver metastases * creatinine within normal institutional limits OR * creatinine clearance \> 50 mL/min for patients with creatinine levels above institutional normal * potassium ≥ lower limit of normal * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) for the duration of study participation and for 4 weeks after the final administration of study drugs. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. * Ability to understand and the willingness to sign an IRB-approved informed consent document. Exclusion Criteria * Known active (untreated) central nervous system (CNS) metastases that require steroids. Subjects with CNS metastases who have completed a course of therapy would be eligible for the study provided they are clinically stable for at least 2 weeks before study entry, defined as: * No evidence of new or enlarging CNS metastasis or new neurological symptoms attributable to CNS metastases. * Asymptomatic and receiving either no or stable doses of anticonvulsants and total doses of corticosteroids equivalent to 10 mg of prednisone or less. * Current or previous other malignancy within 2 years of study entry, except cured basal or squamous cell skin cancer, superficial bladder cancer, prostate intraepithelial neoplasm, carcinoma in situ of the cervix, or other noninvasive or indolent malignancy without sponsor approval. * History of previous exposure to an anti PD1/PD-L1 agent * Patients receiving any other investigational agents and or more than two different chemotherapy regimens for treatment of metastatic disease. * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to a previously administered agent. * Note: Subjects with ≤ Grade 2 neuropathy are an exception to this criterion and may qualify for the study. * Note: If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to pembrolizumab, paclitaxel or carboplatin. * Current uncontrolled cardiac disease such as angina or myocardial infarction, congestive heart failure including New York Heart Association functional classification of 3, or arrhythmia requiring treatment. * History of pneumonitis or active lung infection. * Chronic or current active infectious disease requiring systemic antibiotics, antifungals, or antivirals. * Patients receiving chronic steroids and or immunosuppression. * Known HIV infection, Hepatitis B virus (HBV) or hepatitis C virus (HCV) viremia or at risk for HBV reactivation. HBV DNA and testing for HCV RNA must be undetectable. At risk for HBV reactivation is defined as hepatitis B surface antigen positive or anti-hepatitis B core antibody positive. * History of autoimmune disease(s). * Psychiatric illness/social situations that would limit compliance with study requirements. * Any other condition or circumstance that could interfere with adherence to the study's procedures or requirements, or otherwise compromise the study's objectives such as history of, or any evidence of active, non-infectious pneumonitis. * Has an active infection requiring systemic therapy. * Pregnant women are excluded from this study because of the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants, breastfeeding should be discontinued prior to study entry.