Additive manufacturing has enabled the production of materials with extraordinary behaviors that do not naturally occur. Mechanical metamaterials, which are formed from a repetitive distribution of a lattice structure, can be referred to as a common example of such materials. Due to the high computational cost of direct numerical simulations for structures made of metamaterials, using computational homogenization methods, such as FE2, is inevitable. In the present work, based on the FE2 homogenization scheme, two boundary value problems (BVPs) are solved at two adequately separated scales. As at each macroscopic integration point a representative volume element (RVE) needs to be solved, the finite element discretization of both scales (i.e., the macro-scale structure and the micro-scale lattice) has a huge impact on the computational cost. Although 3D models yield more reliable results, truss-based lattice structures can be modeled using structural beam elements rather than 2D and 3D continuum solid elements. As a result, the number of degrees of freedom for the RVE will decrease from hundreds of thousands to tens. In this study, the applicability of beam elements to model the micro-level lattice structure in the two-scale FE2 homogenization framework is investigated. The accuracy of the model is investigated by comparing the results with direct numerical simulations as well as the homogenized model with continuum solid elements.