Sandwich beams featuring additively manufactured (AM) lattice cores offer exceptional stiffness-to-weight ratios; however, their mechanical response is characterized by complex transverse shear effects that challenge classical modeling approaches. This work investigates the static response of sandwich beams with AlSi10Mg lattice cores and composite or metallic facesheets subjected to both sinusoidal (SDL) and uniformly distributed loads (UDL). Analytical formulations based on First-Order Shear Deformation Theory (FSDT) [1], Third-Order Shear Deformation Theory (TSDT) [2], and Refined Zigzag Theory (RZT) [3] are derived and systematically compared against high-fidelity 3D Finite Element Models (3D-FEM). The lattice core is represented using homogenized equivalent properties derived from unit cell numerical homogenization. Parametric studies examine the influence of core topology, facesheet lamination, and geometric aspect ratios on displacement and stress fields. The results demonstrate that the homogenized core model accurately captures the global deflection response of explicit lattice-core simulations, enabling efficient parametric analyses. Across the investigated geometric ratios and core stiffness levels, RZT consistently provides the most accurate displacement predictions and shows robust agreement with 3D-FEM results under both SDL and UDL. In contrast, FSDT and TSDT capture overall stress trends reasonably well but may exhibit noticeable deviations in deflection for shear-dominant configurations and composite facesheets. The findings provide guidance for the selection of appropriate beam theories in the analysis and design of AM lattice-core sandwich structures.