The pyramid-type lattice sandwich panel is known for its exemplary mechanical characteristics. In this study, we draw inspiration from the local resonance mechanisms observed in acoustic metamaterials and introduce a resonant ring to enhance the capabilities of the panel for damping low-frequency vibrations. We use the finite element method to develop a model to explore the band structure and the corresponding vibrational responses, with a particular emphasis on the significant influence of the bandgap. A comprehensive comparison between the results of experiments and those of simulations unequivocally validated our proposed model. Crucially, our findings underscore that the damping-related effect can be enhanced and the desired range of frequencies can be fine-tuned by appropriately selecting the geometric and periodic parameters of the lattice sandwich panel. These insights have important implications for tailoring materials to specific engineering applications.