We use an extension of fundamental measure theory to lattice hard-core fluids to study the phase diagram of two different systems. First, two-dimensional parallel hard squares with edge-length sigma=2 in a simple square lattice. This system is equivalent to the lattice gas with first and second neighbor exclusion in the same lattice, and has the peculiarity that its close packing is degenerated (the system orders in sliding columns). A comparison with other theories is discussed. Second, a three-dimensional binary mixture of parallel hard cubes with sigma(L)=6 and sigma(S)=2. Previous simulations of this model only focused on fluid phases. Thanks to the simplicity introduced by the discrete nature of the lattice we have been able to map out the complete phase diagram (both uniform and nonuniform phases) through a free minimization of the free energy functional, so the structure of the ordered phases is obtained as a result. A zoo of entropy-driven phase transitions is found: one-, two- and three-dimensional positional ordering, as well as fluid-ordered phase and solid-solid demixings. (C) 2003 American Institute of Physics.