We introduce a nonlocal on-lattice version of density functional theory (DFT) that allows for efficient modeling of fluids in complex inhomogeneous materials. In its previous implementations, classical DFT has required fine discretization of the fluid density. As a result, in studies of gas adsorption it has been used only in idealized pore models with high symmetry. Our new lattice DFT dramatically reduces the computational demand required to model simple fluids and hence can be efficiently applied to complex materials with multiple directions of asymmetry. We apply our new lattice DFT to study nitrogen adsorption in a slit pore with open ends and directly obtain the correct desorption hysteresis. We also apply our DFT to predict hydrogen adsorption accurately in an atomistic model of a metal-organic framework.