The previously developed formalism for the calculation of asymptotic properties of multistate random walks is used to study random walks on several inhomogeneous periodic lattices, where the periodically repeated unit cell contains a number of inequivalent sites, as well as on lattices with a random distribution of inequivalent sites. We concentrate on the question whether the random walk properties depend on the spatial arrangement of the sites in the unit cell, or only on the number density of the different types of sites. Specifically we consider lattices with periodic and random arrangements of columns and lattices with periodic and random arrangements of anisotropic scatterers.