Lattice materials exhibit a high stiffness-to-mass ratio and offer considerable potential for engineering applications. This contribution investigates their use in shell structures, focusing on microstructures with a periodic arrangement of identical unit cells. While the geometric complexity of lattice architectures has long posed a manufacturing challenge, recent advances in additive manufacturing now enable the efficient and precise fabrication of highly complex microstructures. As a result, the numerical modelling of their mechanical behaviour has become increasingly important. Although direct simulation of the full structure provides detailed insight, it is associated with substantial computational cost. Among the efficient alternatives offered by hierarchical multiscale approaches, an FE2-based model is considered here. In the FE2 framework, finite element analyses on the macro- and microscale are coupled. Classical formulations employ continuous models on both scales (e.g., Miehe and Koch [5]), and extensions to continuous macrostructures with lattice-like microstructures have been proposed (e.g., Danesh et al. [1]). By contrast, the combination of structural models at the macroscale with a continuous microstructure is a more recent development (e.g., Geers et al. [2], Gruttmann and Wagner [3], Klarmann et al. [4]). A key aspect of this approach is the special treatment of the representative volume element (RVE), which distinguishes between physical and model boundaries and requires constraints to ensure RVE-size-independent homogenised properties. The present work adopts this modelling strategy and extends it to lattice-type microstructures. The procedure for constructing the representative volume element from the underlying lattice is presented, with the RVE modelled using finite truss or beam elements and incorporating constraints originally developed for continuous microstructures. Finally, the performance of the proposed FE2 model is demonstrated through selected numerical examples and validated against direct numerical simulations.