Recent experimental results have demonstrated that polymeric ionic liquids doped with Li salts exhibit enhanced ionic mobilities and lithium ion transference numbers with increasing salt concentrations. In this study, we used atomistic molecular dynamics simulations on a model system of lithium salt-doped 1-butyl-3-methyl-imidazolium bistriflimide ionic liquids and poly(1-butyl-3-methyl-imidazolium bistriflimide) electrolytes to identify the molecular mechanisms underlying such findings. Our results mirror qualitatively the experimental results on the influence of salt doping on the ion mobilities. Further, a surprisingly stronger dependence (coupling) between the lithium ion mobilities and polymer segmental dynamics is observed relative to the coupling between the anion diffusivities and polymer dynamics. We present results for ion coordination and hopping characteristics to rationalize such behaviors and identify the mechanistic origins of the properties of this emerging class of polymer electrolytes.