Herein, a multiscale tool is developed to design 3D periodic lattice structures. This work aims to solve 3D macro-scale structural design problems by filling the domain with tailored micro-cells to form a design assembly. This multiscale approach follows a macroscale free-material optimization (FMO) method which is followed by micro-scale inverse homogenization methods. The ideal orthotropic material properties of a 3D macro-domain, previously determined with the FMO algorithm, represents a homogenized micro-cell. The material distribution of the micro-structure is obtained through two structural optimization algorithms. Firstly, a derivative-free algorithm is developed to find the ideal material distribution in the form of a slender beam-based lattice unit structure [1]. This method combines Genetic and Particle Swarm Optimization Algorithms and allows multiobjective optimization for 3D elasticity and unidirectional energy absorption. Secondly, the material distribution of the micro-cell is obtained through the level-set method [2] by designing elasticity tensor components under volume constraint. In both cases, FE2 is assumed to couple the micro and macro-scales, and periodic boundary conditions are applied to derive the effective properties of the metamaterial. Powder bed fusion process, an additive manufacturing technology with high design freedom, is used to manufacture demonstrator samples and compression specimens of the optimized multiscale lattice structures. The stiffness, nonlinear unidirectional crushing and lightweight performance of the optimized multiscale designs are benchmarked with well-known standard lattice structures and a full-scale SIMP topology-optimized problem via FE crushing simulation of the lattice assembly and experimental characterization of compression specimens.