We present an extensive molecular dynamics (MD) simulation study of the lithium ion transport in ternary polymer electrolytes consisting of poly(ethylene oxide) (PEO), lithium-bis(trifluoromethane)sulfonimide (LiTFSI), and the ionic liquid N-methyl-N-propylpyrrolidinium bis(trifluoromethane)sulfonimide (PYR13TFSI). In particular, we focus on two different strategies by which the ternary electrolytes can be devised, namely by (a) adding the ionic liquid to PEO20LiTFSI and (b) substituting the PEO chains in PEO20LiTFSI by the ionic liquid. To grasp the changes of the overall lithium transport mechanism, we employ an analytical, Rouse-based cation transport model (Maitra et al. Phys. Rev. Lett. 2007, 98, 227802), which has originally been devised for binary PEO-based electrolytes. This model distinguishes three different microscopic transport mechanisms, each quantified by an individual time scale. In the course of our analysis, we extend this mathematical description to account for an entirely new transport mechanism, namely, the TFSI-supported diffusion of lithium ions decoupled from the PEO chains, which emerges for certain stoichiometries. We find that the segmental mobility plays a decisive role in PEO-based polymer electrolytes. That is, whereas the addition of the ionic liquid to PEO20LiTFSI plasticizes the polymer network and thus also increases the lithium diffusion, the amount of free, mobile ether oxygens reduces when substituting the PEO chains by the ionic liquid, which compensates the plasticizing effect. In total, our observations allow us to formulate some general principles about the lithium ion transport mechanism in ternary polymer electrolytes. Moreover, our insights also shed light on recent experimental observations (Joost et al. Electrochim. Acta 2012, 86, 330).