Discovering materials with intrinsically low lattice thermal conductivity kappa(lat) is an important route for achieving high thermoelectric performance. In reality, the conventional synthetic approach, however, relies on trial and error. Herein, we proposed a new crystallographic parameter, namely the site occupancy factor, as an effective indicator to identify a material catalogue with low kappa(lat). Taking Cu6Te3S, in which some Cu atoms show partial occupancy, as the representative sample, it was found that this compound exhibited ultralow kappa(lat) with weak temperature dependence from 5 K to 350 K. The appearance of a boson peak and unusual two-level tunneling states in the heat capacity measurement revealed the low-lying optical modes and dynamic diffusion disorder, respectively. This glass-like thermal property in a crystalline material arose from the combination of the anharmonic and anisotropic vibration of the Cu atom, the ionic bond feature around the Cu atom, and the global weak bonding, confirmed by the calculated phonon dispersion, electron localization function, and potential energy curves. Utilizing the proposed indicator of partial occupancy, we searched in the Crystallography Open Database for further potential candidate materials with low kappa(lat). As a further test of the efficacy of this strategy, two unearthed compounds were synthesized and both were indeed found to exhibit very low kappa(lat), around 0.6 W m(-1) K-1 at 300 K. Our work explored the close relationship between crystallography and thermal property in crystalline materials and revealed the impact of partial occupancy in complex lattice dynamics, opening up new avenues towards discovering materials with low kappa(lat).