Additive Manufacturing (AM) enables the production of geometrically complex parts that are difficult to manufacture by other means. However, conventional CAD systems are limited in the representation of such parts. This issue is exacerbated when lattice structures are combined or embedded within a complex geometry. This paper presents a computationally efficient, voxel-based method of generating lattices comprised of practically any cell type that can conform to an arbitrary external geometry. The method of conforming involves the tessellation and trimming of unit cells that can leave ‘hanging’ struts at the surface, which is a possible point of weakness in the structure. A method of joining these struts to form an external two dimensional lattice, termed a ‘net-skin’ is also described. Traditional methods of manufacturing lattice structures generally do not allow variation of cell properties within a structure; however, additive manufacturing enables graded lattices to be generated that are potentially more optimal. A method of functionally grading lattices is, therefore, also described to take advantage of this manufacturing capability.