This contribution presents an efficient framework to accelerate the analysis and parametric shape optimization of complex lattice structures. We are interested in exploring on-the-fly shape variations at the unit cell level of these structures to optimize their design and overall performance. To this end, we leverage multiscale geometric models within an isogeometric framework and a dedicated solver that is tailored to the underlying problem at hand [1]. The main idea is to combine reduced order models with domain decomposition, thus allowing an efficient offline/online split of the simulation process [2]. In the offline phase, we construct parametric reduced order models that allow fast evaluations of the local equilibrium at the unit cell level. These reduced models are then coupled in the online phase, while an iterative solver is employed for the solution of the interface problem to obtain the global equilibrium of the full structure. The advantage of this approach is twofold: it not only accelerates structural analysis but also enhances parametric shape optimization using gradient-based algorithms, as the computation of sensitivities at the unit cell level becomes inexpensive. Numerical examples of linear elastic problems show the accuracy and computational efficiency of this approach. [1] Hirschler T., Bouclier R., Antolin P., Buffa A., Reduced order modeling based inexact FETI-DP solver for lattice structures, International Journal for Numerical Methods in Engineering, Vol. 125 (8): e7419, 2024. [2] Chasapi M., Antolin P., Buffa A., Reduced order modeling of non-affine problems on parameterized NURBS multi-patch geometries, Lecture Notes in Computational Science and Engineering, Vol. 151, pp. 67-87, 2024.