We examine the lattice thermal conductivities (κ l ) of Li 2 X (X=O, S, Se, Te) using a firstprinciples Peierls-Boltzmann transport methodology. We find low κ l values ranging between 12and 30 W/m-K despite light Li atoms, a large mass difference between constituent atoms and tightly bunched acoustic branches, all features that give 'high κ l ' in other materials including BeSe (630 W/m-K), BeTe (370 W/m-K) and cubic BAs (3170 W/m-K). Together these results suggest a missing "ingredient" in the basic guidelines commonly used to understand and predict κ l . Unlike typical simple systems (e.g., Si, GaAs, SiC), the dominant resistance to heat-carrying acoustic phonons in Li 2 Se and Li 2 Te comes from interactions of these modes with two optic phonons. These interactions require significant bandwidth and dispersion of the optic branches, both present in Li 2 X materials. These considerations are important for the discovery and design of new materials for thermal management applications, and give a more comprehensive understanding of thermal transport in crystalline solids.