The recently developed dynamic percolation theory is used to solve the problem of diffusion of interacting particles in lattice-gas models within an effective medium approximation. The approach is based on the observation that the motion of a tracer particle in a system of (similar or different) particles can be viewed as particle motion in a changing random environment. This makes it possible to use effective medium theory (EMT) solutions to the latter problem. The main conceptual problem of this approach is to relate the characteristic microscopic times for the evolution of the disordered background to the macroscopic diffusion. We discuss and compare several possible ansatzs for this relation and conclude that relating these times to the chemical diffusion rate is the most reasonable simple choice. Using this ansatz, we obtain EMT approximations for the tracer diffusion coefficient in the noninteracting lattice-gas (NILG, blocking interactions only) model and an approximate EMT relation between the chemical and the tracer diffusion coefficients in a lattice gas with nearest-neighbor interactions. Agreement with available simulation results is good whenever single bond EMT is expected to be reliable.