Evaporative lithography using latex particle templates is a novel approach for the self-assembly of suspension-dispersed nanoparticles into ordered microwire networks. The phenomenon that drives the self-assembly process is the propagation of a network of interconnected liquid bridges between the template particles and the underlying substrate. With the aid of video microscopy, we demonstrate that these liquid bridges are in fact the border zone between the underlying substrate and foam films vertical to the substrate, which are formed during the evaporation of the liquid from the suspension. The stability of the foam films and thus the liquid bridge network stability are due to the presence of a small amount of surfactant in the evaporating solution. We show that the same type of foam-film-stabilized liquid bridge network can also propagate in 3D clusters of spherical particles, which has important implications for the understanding of wet granular matter.