We develop a coarse-grained lattice gas model to describe drying-mediated self-assembly of nanoparticles in three-dimensions (3D). Our model is an extension of the model developed by Rabani et al. [Nature 426, 271 (2003)] in two-dimensions (2D). We show that when liquid evaporation occurs layer-by-layer and solvation forces are strong, the resulting morphologies agree well with the predictions of the 2D model. We discuss scenarios in which the full 3D treatment is necessary, and predict the formation of nano-stalagmites.