Polymer lithium single-ion conductors, i.e., ionomers, are promising solid electrolyte materials for battery applications. Adding an organic co-cation into these polymer electrolytes can lower the glass transition temperature and decrease the interactions between the tethered backbone anion and the lithium, leading to improved lithium ionic conductivity. Here we conduct a computational investigation on how three ammonium based co-cations, differentiated in size and structure, affect lithium-ion dynamics in an ionomer electrolyte. Our results show that the lithium-ion hopping has a close relationship with lithium coordination structures and could be enhanced by adding the organic co-cation. Ionic conductivity, however, depends not only on lithium hopping frequency but also on polymer morphology; an interconnected or percolating ionic aggregate structure appears to favour a more continuous lithium-ion hopping process, whereas the larger sized organic co-cations can hinder this transport.