This is a phase 1b/2 study, designed to evaluate the safety, tolerability, and efficacy of VX15/2503 in combination with avelumab in immunotherapy-naïve subjects diagnosed with advanced (stage IIIB/IV) NSCLC who have either progressed on cytotoxic chemotherapy or declined first-line treatment with cytotoxic chemotherapy. The primary objective (Dose Escalation Phase) is to evaluate the safety and tolerability of ascending doses of VX15/2503 Q2W in combination with avelumab 10mg/kg Q2W. The second primary objective (Dose Expansion Phase) is to evaluate safety and tolerability of teh recommended phase 2 dose of VX15/2503 administered in combination with 10 mg/kg avelumab Q2W. The secondary objectives include (Dose Expansion Phase), a preliminary estimate of efficacy using the following in accordance with Response Evaluation Criteria in Solid Tumors (RECIST) 1.1, Objective Response (OR), Duration of Response (DoR) and Progression-Free Survival (PFS), as well as making a preliminary estimate of efficacy using the following in accordance with iRECIST, OR, DoR and PFS. Additional secondary objectives are to characterize the pharmacokinetics profile of VX15/2503 and avelumab administered Q2W in combination, evaluate the immunogenicity of VX15/2503 and avelumab administered Q2W and evaluate VX15/2503 and avelumab pharmacodynamics markers including but not limited to receptor occupancy. Exploratory objectives include identification of candidate biomarkers of activity and biomarkers that may predict response to treatment with combination therapy of VX15/2503 and avelumab.