The basic theoretical structure of all lattice theories for polymer solutions suggests that they will become increasingly accurate as the coordination number of the lattice is increased. Monte Carlo simulations have been performed for polymer chains of length 10 and 40 with monomeric solvent on three-dimensional body-centered cubic (BCC) and face-centered cubic (FCC)lattices. The energies of mixing and radii of gyration have been obtained and compared with standard lattice theories. The simulation data show that higher-order energetic terms are more significant on the high coordination number lattices than on the simple cubic lattice, in apparent contradiction to conventional wisdom. For the quantities considered, common lattice theories are shown to be no better for BCC and FCC lattices than was established in previous tests against simulations conducted on simple cubic lattices.