Phase II Trial of Continuation Therapy in Advanced NSCLC

Inclusion Criteria: Subjects must meet all of the following applicable inclusion criteria to participate in this study: * Written informed consent and HIPAA authorization for release of protected health information. * Age ≥ 18 years at the time of consent. * Histological or cytological evidence of stage IV NSCLC (any histology) * Subjects must have progressed on or after previous platinum-based chemotherapy. Chemotherapy may have previously been given with a PD-1 or PD-L1 inhibitor. Subjects must have also progressed on or after receiving any PD-1 or PD-L1 inhibitor (including pembrolizumab) as their most recent therapy and must have had at least a 3-month PFS on this therapy. * Subjects must be enrolled on the trial within 6 weeks of their last infusion of PD-1 or PD-L1 inhibitor therapy. * Subjects whose tumors harbor a mutation in EGFR exon 19 or 21 or have gene rearrangements in ALK or ROS1 must have already been treated with standard targeted therapies. NOTE: Subjects must also have progressed on or after platinum-containing combination chemotherapy. * ECOG Performance Status of 0 or 1 within 28 days prior to registration for protocol therapy. * Must be fit enough to receive next-line chemotherapy (either gemcitabine, docetaxel, or pemetrexed \[non-squamous only\]) according to the discretion of the treating physician. * Adequate laboratory values obtained within 28 days prior to registration for protocol therapy. * Women of childbearing potential (WOCBP) must have a negative urine or serum pregnancy test within 7 days prior to study registration and/or within 72 hours of first dose of study drugs. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * Women of childbearing potential must be willing to use two methods of contraception or abstain from heterosexual activity from the point of registration through 120 days after the last dose of study drug. * Male subjects capable of fathering a child must agree to use an adequate method of contraception starting with the first dose of the study drug through 120 days after the last dose of the study drug. Exclusion Criteria: Subjects meeting any of the criteria below may not participate in the study: * Pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment. * Active central nervous system (CNS) metastases. NOTE: Subjects who are symptomatic or have not undergone prior brain imaging must undergo a head computed tomography (CT) scan or brain MRI within 28 days prior to registration to exclude brain metastases. * Treatment with any investigational agent within 28 days prior to registration for protocol therapy with the exception of PD-1 or PD-L1 inhibitors. * No active second cancers with the exception of localized non-melanoma skin cancer, in-situ cervical or in-situ bladder cancer. * Evidence of active autoimmune disease requiring systemic treatment within the past 90 days or a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids or immunosuppressive agents. * History of (non-infectious) pneumonitis requiring treatment with corticosteroids, evidence of interstitial lung disease or active, non-infectious pneumonitis. * History of an immune-related toxicity requiring treatment with corticosteroids during prior PD-1/ PD-L1 inhibitor treatment. * Diagnosis of immunodeficiency or is receiving chronic systemic corticosteroid therapy or other immunosuppressive therapy (excludes inhaled corticosteroids) within 7 days of study registration. * History of psychiatric illness or social situations that would limit compliance with study requirements. * Clinically active infection (≥ Grade 2) as judged by the site investigator. * Known history of human immunodeficiency virus (HIV) infection or chronic hepatitis B or C. NOTE: HIV, HBV or HCV testing is not required. * 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 site investigator. * Known history of active TB (Bacillus Tuberculosis). * History of hypersensitivity to pembrolizumab, docetaxel, gemcitabine, pemetrexed or any of their excipients. * Has received a live vaccine within 30 days prior to planned start of study therapy.