The wetting of a solid substrate by a lyotropic sponge phase is studied by using grazing X-ray scattering and optical microscopy. The wetting promotes the formation of an anisotropic layer of tetragonal symmetry on length scales of similar to10 nm on the substrate. The topology of the substrate defines the orientation of the symmetry axis of this induced surface layer. The shape anisotropy characteristics of the tetragonal lattice experimentally obtained account for the optical phase shift measured.