Integer lattices from non-binary low-density codes are considered for communication over the Gaussian channel. Finite constellations are built via the Voronoi region of a dense small-dimensional sub-lattice. We show how mapping and demapping for these Voronoi constellations are performed with a linear complexity in the blocklength. As an example, we present Leech Constellations that involve Construction-A lattices as fine lattices and a direct sum of multiple copies of the Leech lattice for shaping.