In wireless sensor networks, real-time data delivery schemes typically achieve a desired delivery speed by proactively performing one-hop lookahead. Recently, to reduce the deadline miss ratio against the desired delivery speed, a study has proposed a real-time routing protocol based on proactively performing twohop lookahead. However, the recent study might cause heavy message exchange overhead and high computing complexity to proactively carry out obtainment of two-hop neighborhood speed information in the entire sensor network whether data are delivered or not. Moreover, although multi-hop lookahead provides the least deadline miss ratio, due to the restriction from the overhead and the complexity, the recent study merely adopts the two-hop lookahead manner. In this paper, we propose a novel real-time routing protocol. The proposed routing protocol adopts on-demand neighborhood information obtainment only around data forwarding paths. The on-demand information obtainment is performed in multi-hop lookahead. Hence, the proposed routing protocol is able to provide the least deadline miss ratio to realtime data delivery. Simulation results prove that the proposed routing protocol offers better performances with respect to deadline miss ratio, total communication costs, energy efficiency, and network lifetime.