Additive Manufacturing (AM) constitutes today a reality for the fabrication of high-performance lattice structures. This increasing interest in those complex structures raises however the issue of simulating them as standard numerical methods and models need overwhelming computational resources in this context. Built upon multiscale geometric models, we introduce a dedicated isogeometric approach that takes advantage of the specific nature of the underlying problem. More specifically, we combine model order reduction strategies together with domain decomposition solvers. In an offline stage, we build reduced spaces that enable to quickly solve the static equilibrium of unit cells. In the online stage, we evaluate the global equilibrium of the full structure via a FETI-like approach : the reduced order models of the cells composing the structures interact through interface loads which are iteratively updated by a krylov solver until the coupling conditions between these cells are fulfilled. More than just being an interesting approach for performing the structural analysis of lattice structures, we show how it provides an efficient framework for solving structural optimization of those complex structures. Indeed, the local ROMs associated to the cells provide cost-effective sensitivity analyses. Thus, gradient-based optimization algorithms can be appropriately used to obtain the optimal distribution of cell-level shape parameters within the lattice structures to enhance their overall mechanical performances.