The Study of NC318 Alone or in Combination With Pembrolizumab in Patients With Advanced Non-small Cell Lung Cancer

Inclusion Criteria: * Histologically or cytologically documented, locally advanced or metastatic (i.e., Stage IIIB not eligible for definitive chemoradiotherapy, Stage IV, or recurrent) NSCLC (per the American Joint Committee /AJCC staging system) * ECOG performance status of 0 to 1 * Measurable disease per RECIST v1.1 criteria * Arm 1a, and 1b and 1c: Prior PD-1 axis inhibitor therapy (anti-PD-1 or anti-PD-L1, e.g. nivolumab, pembrolizumab, atezolizumab, durvalumab, avelumab) either alone or in combination with other systemic agents, with documented progressive disease. * Arm 2a: PD-L1 expression of less than 50 percent (PD-1 axis inhibitor therapy naïve) * Patients with NSCLC known to harbor an ALK rearrangement, ROS1 rearrangement, EGFR mutation or BRAF mutation known to be sensitive to FDA approved tyrosine kinase inhibitors (TKI), are only eligible after experiencing disease progression (during or after treatment) or intolerance to respective TKI: 1. Patients with TKI treated EGFR mutant NSCLC harboring the secondary EGFR T790M tumor must have received prior osimertinib. 2. Patients with crizotinib treated ALK rearranged NSCLC must have received a next generation ALK inhibitor (e.g. ceritinib, alectinib, brigatinib or lorlatinib). * At least one tumor amenable to incisional, excisional, core or forceps (transbronchial) biopsy. Patients must be willing to undergo a tumor biopsy before starting trial therapy and at the time of disease progression. * Adequate hematologic and end-organ function Exclusion Criteria: * Subjects must not have a history of life-threatening toxicity related to prior anti-PD-1 axis therapy: a. Subjects with history of anti-PD-1 axis therapy toxicities that are unlikely to recur with standard countermeasures (e.g., hormone replacement after adrenal crisis) are eligible. * Symptomatic or untreated CNS metastases. Patients with a history of treated asymptomatic CNS metastases are eligible, provided they meet all of the following criteria: 1. No evidence of interim progression between the completion of CNS-directed therapy and the start of trial therapy 2. No ongoing requirement for dexamethasone as therapy for CNS disease; anticonvulsants at a stable dose are allowed. 3. Completed stereotactic radiosurgery at least 1 week prior to initiation of trial therapyCycle 1, Day 1 or whole-brain radiation at least 2 weeks prior to initiation of trial therapyCycle 1, Day 1. * History of leptomeningeal carcinomatosis * Prior palliative radiotherapy outside the CNS within 2 weeks of the first dose of study drug * Treatment with systemic immunosuppressive medications (including but not limited to, dexamethasone at doses \> 2 mg daily (or equivalent dose of other corticosteroids), cyclophosphamide, tacrolimus, sirolimus, azathioprine, methotrexate, thalidomide, and antitumor necrosis factor \[anti-TNF\] agents) within 2 weeks prior to initiating trial therapy. (Inhaled or topically applied steroids, and acute and chronic standard-dose NSAIDs are permitted. Replacement steroids are also permitted). Prophylactic corticosteroids prior to imaging with intravenous contrast are allowed per institutional guidelines, without need for delay of 2 weeks. Arm 2a: No prior PD-1 axis inhibitor therapy