With increasing connectivity and sophisticated software, modern vehicles are able to leverage different kinds of services provided by the environment. One such service recommended by the Automotive Edge Computing Consortium (AECC) is downloading high-definition map data by vehicles. This high volume of data can be provided to the vehicles when moving by pre-allocating resources on edge server nodes or roadside units if the routes are known apriori. However, this is not a realistic assumption to make in general. Therefore, in this work, we propose a two-stage optimization framework for efficient data delivery to connected vehicles via edge nodes while considering dynamic route changes. We have evaluated the efficiency of this proposed approach (considering a real-world dataset) with respect to (a) offline optimization strategies considering fixed routes and (b) a greedy approach considering route changes. Our proposed approach works considerably better than the existing approaches in the context of dynamic route changes.