Additive Manufacturing (AM), specifically Laser Powder Bed Fusion (LPBF), may enable the production of geometrically complex structures with a combination of high specific strength, ideal for weight-saving structural applications in aeronautics as well as the biomedical industry. Body-Centered Cubic (BCC) lattice structures as well as structures in the class of Triply Periodic Minimal Surfaces - TPMS, the Gyroid structures, show excellent mechanical properties in terms of specific strength and energy absorption capacity along with minimal weight as well as minimized stress concentration. Despite the abundance of scientific research, the mechanical properties of LPBF-produced Lattice and Gyroid structures are difficult to predict, mainly as a consequence of additive manufacturing-induced microstructural change and residual stress. Such process-induced behaviors strongly depend on scan path, build orientation, and thermal gradients during printing. A multi-scale strategy was proposed in this research, combining experimental tests at nano- and macro-scale with numerical simulations. Local mechanical properties were explored through nano-indentation experiments on samples with varying characteristic dimensions, in order to check potentially size-dependent mechanical responses. In addition, metallographic examinations and Finite Element Method (FEM) simulations were made in order to examine and quantify residual stress impact, heat treatment, and their effect on the sample's microstructure, as well as local mechanical properties. The obtained results demonstrate the presence of size-effects, as well as the residual stress effect on mechanical response of LPBF manufactured lightweight components, and confirm how a local and multi-scale approach is necessary for their optimal design. The proposed methodology proved to be highly accurate and can be used effectively for the optimized design of the components produced by AM.