The advancement of technologies such as additive manufacturing, combined with topology optimization techniques, led to the creation of innovative lattice structures with a broad range of applications, from aerospace to the chemical industry. However, solving these structures using the Finite Element Method (FEM) presents significant computational challenges, particularly when dealing with large-scale systems in 3D geometries. Traditional direct solvers struggle with the memory and time demands of these problems, making iterative solvers the only feasible alternative. To address the computational burden of numerical simulations, Reduced Order Models (ROMs) have been developed to offer faster solutions, though they typically come at the cost of losing some accuracy. In this work, we propose a novel approach by integrating the Empirical Interscale Finite Element Method (EIFEM) [1] into an iterative scheme as preconditioner. This strategy aims to accelerate the iterative solution process while maintaining the accuracy of the full FE method. We present numerical examples demonstrating the effectiveness of this approach.