We investigate the synchronization process in a Kuramoto model of phase-coupled oscillators with distance-dependent delay. The oscillators occupy the nodes of a two-dimensional square lattice subjected to periodic boundary conditions. The mean-field interactions with velocity-dependent delays propagate along the lattice sites. This gives rise to a non-uniform distribution of delays and lattice dimensionality dependence, which is not present in mean-field models without delays. We find that the 'coupling strength-delay' phase diagram does not show up reentrant behavior present in models with uniform delay. A number of dynamic patterns, reported earlier for a generalized Kuramoto model with non-mean-field distance-dependent interactions, is also found.