The lattice Boltzmann method (LBM) has been proved to be a useful tool in many areas of computational fluid dynamics, including computational aero-acoustics (CAA). However, for historical reasons, its applications in CAA have been largely restricted to simulations of isothermal (Newtonian) sound waves. As the recent kinetic theory-based reformulation establishes a theoretical framework in which LBM can be extended to recover the full Navier–Stokes–Fourier (NS) equations and beyond, in this paper, we show that, at least at the low-frequency limit (sound frequency much less than molecular collision frequency), adiabatic sound waves can be accurately simulated by the LBM provided that the lattice and the distribution function ensure adequate recovery of the full NS equations.