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This paper presents a semi-analytical approach to analyze the dynamic response characteristics of lattice composite sandwich plates with varying lattice truss cores. Under the premise of satisfying the classical laminate theory assumptions of Allen, the lattice truss core is considered an equivalent homogenized structure. Then, the displacement equations for the sandwich plate utilize the first-order shear deformation theory (FSDT). The energy equation for the sandwich plate is constructed using the Lagrange energy method and solved through the Rayleigh–Ritz method. To mimic arbitrary boundary conditions, artificial boundary spring techniques are utilized. The spectral geometry method (SGM) is utilized to describe the displacement field of dynamic equations and boundary conditions. Legendre polynomials are chosen to construct admissible displacement functions for the structure, supplemented by auxiliary polynomials to eliminate discontinuities at the boundaries. The method’s validity is verified through comparisons with relevant literature and finite element method (FEM). Based on free vibration analysis, both steady-state and transient displacement responses of laminated composite sandwich plates are examined, considering the influences of structural parameters and boundary conditions on dynamic response characteristics. These works can provide suitable theoretical references for the engineering field. [ABSTRACT FROM AUTHOR]