Breakthroughs in additive manufacturing enable the fabrication of lattice structures which have begun to demonstrate promising applications across a range of industrial sectors. These structures present a well-chosen quasi-periodic distribution of voids and materials that might lead to superior mechanical performance in comparison to more standard homogeneous designs. In particular, they seem to have interesting mechanical properties in the context of structural dynamics, such as vibration control, wave propagation, and dynamic absorbers. Nevertheless, in order to unlock and understand fully the potential of lattice structures, there is a crucial need for numerical models and methods that accurately predict their mechanical responses, especially for structural dynamic applications. There appears to be a degree of uncertainty surrounding the use of multiscale approaches in the context of dynamic analyzes of additively manufactured lattice structures as they require a clear scale-separation, and consequently often restrict the study to low frequencies. As an alternative, recent works introduce dedicated solvers which enable to perform the full volumetric fine-scale simulation of lattice structures with limited numerical resources. This work follows such a strategy by building a dedicated solver for the steady-state dynamic analysis of lattice structures. More specifically, we employ analysis-suitable spline models in the spirit of Elber (2017). Thanks to IsoGeometric Analysis, this provides great analysis accuracy and eases the construction ofreduced order models (ROM), which learn the mechanical behaviors and similarities of the lattice cells. Finally, the intrinsic quasi-periodicity of lattice structures is further exploited by inter-connecting the ROMs through the use of sub-structuring and domain decomposition methods. By effectively solving steady-state dynamics problems, we investigate the vibrational behavior and mechanical performance of lattice structures under realistic loading conditions.