Polyelectrolyte materials are an interesting class of electrolytes for use in fuel cell and battery applications. Poly(para-phenylene terephthalamide) (PPTA, Kevlar) is a liquid crystalline polymer that, when sulfonated, is a polyelectrolyte that exhibits moderate ion conductivity at elevated temperatures. In this work, quasi-elastic neutron scattering (QENS) experiments were performed to gain insight into the effect of the presence of lithium counterions on the chain dynamics in the material. It was found that the addition of lithium ions decreases the dynamics of the chains. Additionally, the binding of lithium ions to the sulfonic acids groups was investigated by density functional theory (DFT) calculations. It was found that the local surroundings of the sulfonic acid group have very little effect on the lithium-ion binding energy. Binding energies for a variety of different systems were all calculated to be around 150 kcal/mol. The DFT calculations also show the existence of a structure in which a single lithium ion interacts with two sulfonic acid moieties on different chains. The formation of such "electrostatic cross-links" is believed to be the source of the increased tendency to aggregate and the reduced dynamics in the presence of lithium ions.