Solid-state batteries, in which solid electrolytes (SEs) replace their liquid alternatives, promise high energy density and safety. However, understanding the relation between SE composi- tion and properties, stemming from intricate interactions among constituent sublattices that involve non-local electronic and nuclear dynamics, remains a critical and unsolved challenge. In this work, we assess a range of state-of-the-art electronic structure methods and show that a density-functional method that accounts for the non-locality and many-body effects in both electronic exchange and correlation interactions provides predictive results for the local structure and diffusion properties of SEs. This is exemplified on the chemical space of argyrodite SEs, specifically those with the chemical formula Li6MS5X (LMSX; M = P, Ge, Si, Sn; X = Cl, Br, I), serving as paradigmatic and challenging test cases. The employed HSE06+MBDNL method unveils how the S/X site disorder and the anionic sublattice gov- ern lithium diffusion across the LMSX compositional space. The disorder at the S/X site determines the number of accessible lithium diffusion channels, while non-local exchange and van der Waals interactions finely adjust the coupling between the framework lattice and mobile lithium, thereby regulating the barrier for Li migration. Consequently, the intricate interplay of non-local electronic interactions in the predictive design of Li-solid electrolytes – and likely many other functional materials – is emphasized.