Motivated by the recent report of superconductivity above 200 K in ultra-dense hydrogen sulfide, we search for high- conventional superconductivity in the phase diagram of the binary Li-S system, using ab initio methods for crystal structure prediction and linear response calculations for the electron-phonon coupling. We find that at pressures higher than 20 GPa, several new compositions, besides the known , are stabilized; many exhibit electride-like interstitial charge localization observed in other alkali-metal compounds. Of all predicted phases, only an fcc phase of , metastable before 640 GPa, exhibits a sizable , in contrast to what is observed in sulfur and phosphorus hydrides, where several stoichiometries lead to high . We attribute this difference to hybridization and avoided core overlap, and predict similar behavior for other alkali-metal compounds.