Dynamic percolation theory is used to obtain the tracer diffusion coefficient in binary mixtures of "noninteracting" lattice gas (with only the blocking interactions, i.e., double occupancy of a lattice site is forbidden) within the effective medium approximation (EMA). Our approach is based on regarding the background particles as a changing random environment. The result is expressed in terms of two fluctuation time parameters which we attempt to determine self-consistently. We compare two possible choices for these parameters which are consistent with our former results for the single component system. The resulting tracer diffusion coefficient for both choices compares well with numerical simulations whenever single bond EMA is expected to be reliable. Comparison is also made with the theoretical results of Sato and Kikuchi [Phys. Rev. B 28, 648 (1983)] and discrepancies between both theories are discussed.