Recent progress in additive manufacturing (AM) allows for printing customized products with multiple materials and complex geometries that could form the basis of multimaterial designs with high performance and novel functions. Effectively designing such complex products for optimal performance within the confines of AM constraints is challenging due to the need to consider fabrication constraints while searching for optimal designs with a large number of variables, which stem from new AM capabilities. In this study, fabrication constraints are addressed through empirically characterizing multiple printed materials' Young's modulus and density using a multimaterial inkjet-based 3D-printer. Data curves are modeled for the empirical data describing two base printing materials and 12 mixtures of them as inputs for a computational optimization process. An optimality criteria (OC) method is developed to search for solutions of multimaterial lattices with fixed topology and truss cross section sizes. Two representative optimization studies are presented and demonstrate higher performance with multimaterial approaches in comparison to using a single material. These include the optimization of a cubic lattice structure that must adhere to a fixed displacement constraint and a compliant beam lattice structure that must meet multiple fixed displacement constraints. Results demonstrate the feasibility of the approach as a general synthesis and optimization method for multimaterial, lightweight lattice structures that are large-scale and manufacturable on a commercial AM printer directly from the design optimization results.