We present a novel lattice modelling approach for the behaviour of nematic liquid crystals in cells. Our model includes elastic deformation energy, finite surface anchoring and applied voltages. These have been implemented and tested in a two-dimensional model. We present results from this model for various analytic test cases and for a real scanning electron micrograph (SEM) surface profile, as employed in experimental work on zenithally bistable nematic devices (ZBN). Finally we discuss, briefly, our extension of the model to three dimensions.