Percolation is investigated using Monte Carlo lattice dynamics on two unusual lattices of sorption sites suggested by recent zeolite simulations. The lattices are modifications of the simple cubic and the tetrahedral lattice. We investigate the percolative behavior caused by these modifications and compare this behavior with that of the parent lattice from published simulation results for simple cubic lattices and the approximate (but analytical) effective medium approximation (EMA) theory. The modifications of the parent lattices include (1) the addition of an octahedral sublattice at each node within a simple cubic superlattice and (2) partial blocking of three adjacent bonds by a single bond-blocker on a tetrahedral lattice. For the former, we examine both random and correlated placement of superlattice bond-blockers. We also examine random placement of sub-lattice bond-blockers. We also investigate the effect of activation energies on percolation. We ascertain to what degree regular lattice percolation behavior holds for the modified lattices, finding that modifications to regular lattices change the general transport behavior in easily predicted ways. This result suggests that regular lattice percolation theory can be relevant and applicable to a wide variety of zeolitic transport problems even when it is not obvious that the zeolite presents a regular lattice of sorption sites.