Understanding the interplay between local structure and dynamics is critical for establishing design rules for advanced ion-conducting electrolytes. In this work, a set of Li-salt in liquid electrolytes is studied using dielectric relaxation spectroscopy (DRS) to examine correlations between several electrolyte properties, including conductivity, dielectric relaxation time and strength, ionicity, and viscosity. These properties were evaluated by changing ion concentration, solvent type, and anion type. DRS was used to identify relaxation processes associated with the solvent and different ion-solvent coordinating structures, and the dielectric properties are reported for the first time for a majority of these systems. The behavior of viscosity and conductivity were shown to change similarly with concentration when accounting for the local coordinating environment, regardless of the salt or solvent type. τα, the dielectric relaxation time of the solvent-ion complexes, is shown to be independent of ion content at low salt concentrations, when solvent separated ion pairs are the dominant ion-solvent complex. However, at high ion concentrations, a new relationship, a power-law dependence, was identified between molar conductivity and τα, as well as viscosity and τα, demonstrating that the dependence of molar conductivity or viscosity on τα is controlled in part by the solvent type, due to variation in shielding between contact ion pairs and aggregates. In contrast, there was not a clear change in the dependence of molar conductivity or viscosity on τα with changing anion. Furthermore, the effective dipole moments of the ion-solvent complexes were determined, and found to decrease with increasing ion concentration, as contact ion pairs and aggregates form. This systematic analysis of the wide range of Li-salts and solvents, and discussion of relations between different local structures and dynamic processes that contribute to conductivity, helps lay a foundation for the design of new liquid electrolytes.