The current development of science and technology has put increased demands on the versatility of metamaterials. In this paper, the band gap characteristics of a lattice metamaterial that can simultaneously modulate thermal expansion and Poisson's ratio are studied, the dispersion characteristics of elastic waves propagating in periodic lattice metamaterials are analyzed, and the effects of different structures and parameters on the band gap are discussed. The results indicate that the configuration has excellent band gap properties while satisfying the tunable coefficient thermal expansion (CTE)and Poisson's ratio functions. Through reasonable material selection and shape design, it is expected to achieve a multi-objective win-win for specific thermal expansion properties, Poisson's ratio, and band gap design, resulting in better tunability and versatility of the metamaterial.