In this paper we present a numerical investigation into surface-based lattice structures with the aim of facilitating their design for additive manufacturing. We give the surface equations for these structures and show how they can be used to tailor their volume fractions. Finite element analysis is used to investigate the effect of cell type, orientation and volume fraction on the elastic moduli of the lattice structures, giving rise to a valuable set of numerical parameters which can be used to design a lattice to provide a specified stiffness. We find the I-WP lattice in the [001] orientation provides the highest stiffness along a single loading direction, but the diamond lattice may be more suitable for cases where lower mechanical anisotropy is important. Our stiffness models enable the construction of a powerful numerical tool for predicting the performance of graded structures. We highlight a particular problem which can arise when two lattice types are hybridised; an aberration leading to structural weakening and high stress concentrations. We put forward a novel solution to this problem and demonstrate its usage. The methods and results detailed in this paper enable the efficient design of lattice structures functionally graded by volume fraction and cell type. Keywords: Additive manufacturing, Lattice structure, Homogenisation, Functional grading