Solid-state batteries, in which solid electrolytes (SEs) replace their liquid alternatives, promise high energy density and safety. However, understanding the relation between SE composition and properties, stemming from intricate interactions among constituent sublattices that involve non-local electronic and nuclear dynamics, remains a critical and unsolved challenge. Here, we evaluate electronic structure methods and demonstrate that a density-functional approach incorporating non-local and many-body effects in exchange-correlation interactions provides predictive results for the local structure and diffusion properties of SEs. Focusing on argyrodite SEs (Li6±xM1±yS5±zXn, LMSX; M = P, Ge, Si, Sn; X = Cl, Br, I), we explore their compositional landscape as a test case. The employed HSE06+MBDNL method unveils how the S/X site disorder dictates the diffusion of lithium by controlling the number and length of the diffusion pathways. Additionally, non-local exchange and van der Waals interactions precisely modulate the coupling between the framework lattice and mobile lithium ions, thereby influencing the migration barrier. Consequently, the interplay of non-local electronic interactions in the predictive design of Li-solid electrolytes – and likely many other functional materials – is emphasized. This study demonstrates the role of non-local exchange and correlation interactions in solid electrolytes (SEs) for lithium-ion batteries. Through analysis of argyrodite SEs, it reveals how non-local interactions influence lithium diffusion and structural stability, guiding future SE design.