The microemulsion model proposed by Ciach, Hoye, and Stell [J. Phys. A 21, L777 (1988)] is a lattice gas model for ternary mixtures of water, oil, and amphiphile, which explicitly takes into account orientational degrees of freedom of amphiphilic molecules. Usually only a discrete set of orientations (towards nearest-neighbor sites) is permitted, and the model is lattice dependent. An investigation about the ground state phase diagram on the body-centered cubic (bcc) and face-centered cubic (fcc) lattices, compared with previously known results on the simple cubic (sc) lattice, is performed. Different structured phases are found, resembling experimentally observed phases and not always considered in the literature. The role of the lattice structure is discussed.