We study wave motion in a lattice differential equation, specifically, in a spatially discrete Allen-Cahn equation with a bistable nonlinearity. The system may, but need not, be near the continuum limit. Superimposed on the regular (periodic) lattice is a spatial variation which varies in an arbitrary (generally non-periodic) fashion; it can either be a variation in the coupling (diffusion) constants between consectutive lattice points, or in the nonlinearities at each point. Existence of generalized traveling waves is shown, as well as phenomena of pinning versus transmission of waves. This is joint work with Shiu-Nee Chow, Kening Lu, and Wenxian Shen.