This study presents an analytical and numerical investigation of the buckling behavior of sandwich plates composed of additively manufactured lattice cores and carbon/epoxy composite facesheets. In the analytical formulation, the sandwich plate is modeled as a multi-layered laminate in which both the facesheets and the homogenized core layer are included within the same higher-order shear deformation plate theory (HSDT) framework, enabling an accurate representation of transverse shear deformation and laminate coupling effects. Several higher-order plate theories are considered to assess their influence on predicted critical buckling loads. Finite element analysis (FEA) is employed to perform three-dimensional eigenvalue buckling analyses, which serve as numerical benchmarks. The lattice core is modeled using beam elements, while the composite facesheets are represented by shell elements. The analytical predictions are compared with the finite element results in terms of critical buckling loads and associated mode shapes. A parametric study is conducted by varying the facesheet layup, including symmetric cross-ply, unsymmetric cross-ply, quasi-isotropic, and angle-ply configurations, as well as the core thickness, in order to investigate their effects on buckling resistance. The comparison is used to evaluate the accuracy and applicability of different higher-order plate theories across a range of laminate configurations and geometric parameters. Overall, the results indicate that HSDT-based analytical models provide buckling predictions that show good agreement with finite element solutions while requiring significantly lower computational effort, making them attractive for preliminary design and parametric studies of lattice-core sandwich plates.