The application of sandwich structures in diverse fields such as rail cars, aircraft, and civil constructions has become widespread due to their numerous advantages, including high performance, low weight, high buckling resistance, excellent thermal insulation, and high specific energy absorption. Due to global competition and the imperative to minimize material consumption and costs, innovative lightweight concepts and technologies are crucial. Additive manufacturing (AM) emerges as a key player due to its design flexibility, enabling the creation of intricate strut-based lattice structures as cores for sandwich panels—a feat unattainable with conventional manufacturing processes. Lattice structures, characterized by intricate geometric patterns, are central to the investigation as they are believed to enhance the structural integrity and efficiency of sandwich panels. In this study, an analytical and numerical analysis of a sandwich structure with a composite facesheet and a lattice core manufactured by additive manufacturing is carried out. This paper aims to analytically calculate the mechanical behavior of the hybrid sandwich structure under three-point bending and to verify the results by the finite element method. The analytical method used in this article for the analysis of the composite sandwich structure is the First-Order Shear Deformation Theory (FSDT) according to Carlsson and Kardomateas and computed in MATLAB. The numerical analysis of the hybrid sandwich structure was performed in ANSYS. In the analyses, homogenized models of lattice structures, which had been previously validated, were employed to reduce the number of elements and thereby save time during the solution process. As a result of the study, an extensive investigation into the deformation, shear, and normal stress values of sandwich structures with lattice cores of varying aspect ratios has been carried out. As a future work, the mechanical behavior of additively manufactured lattice core structure can be analyzed more deeply by using higher-order theories.