The rapid rise of e-commerce is intensifying pressure on last-mile delivery networks, making the strategic placement of parcel lockers an urgent urban challenge. In this work, we adapt multilayer two-mode Social Network Analysis to the parcel-locker siting problem, modeling city-scale systems as bipartite networks linking spatially resolved demand zones to locker locations using only open-source demographic and geographic data. We introduce two new Social Network Analysis metrics, Dual centrality and Coverage centrality, designed to identify both structurally critical and highly accessible lockers within the network. Applying our framework to Milan, Rome, and Naples, we find that conventional coverage-based strategies successfully maximize immediate service reach, but tend to prioritize redundant hubs. In contrast, Dual centrality reveals a distinct set of lockers whose presence is essential for maintaining overall connectivity and resilience, often acting as hidden bridges between user communities. Comparative analysis with state-of-the-art multi-criteria optimization baselines confirms that our network-centric metrics deliver complementary, and in some cases better, guidance for robust locker placement. Our results show that a network-analytic lens yields actionable guidance for resilient last-mile locker siting. The method is reproducible from open data (potential-access weights) and plug-in compatible with observed assignments. Importantly, the path-based results (Coverage centrality) are adjacency-driven and thus largely insensitive to volumetric weights.