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This paper describes a methodology for designing the material distribution and orientation of three-dimensional non-uniform (heterogeneous) lattice structures. Recent advances in additive manufacturing enable fabrication across multiple length scales. Homogenization-based design optimization and the subsequent projection of the optimized design facilitate the synthesis of large-scale microstructures that form lightweight bionic designs. The main aspects of this research are (a) the construction, homogenization-based optimization, and projection of two types of lattices with different degrees of anisotropy and (b) the parallelization of the analysis, optimization, and projection framework in order to handle large-scale meshes and obtain high-resolution, heterogeneous lattice structures. Cubic and octet-truss lattices were selected to demonstrate the ability of the framework to design different types of lattices. A quadcopter arm and an internal wing structure were designed using the optimization and projection framework, verifying its capability to synthesize heterogeneous lattice structures for complex design domains. The ability to change the complexity of optimized microlattices using the characteristic parameters of the lattice is discussed. The relationship between the lattice anisotropy and the optimized, smoothed orientation is investigated, and the optimized design for each lattice is compared with those obtained using conventional design optimization procedures.