Distant retrograde orbits (DROs) in cislunar space offer a promising option for providing navigation services to satellites in the Earth-Moon system due to their long-term orbital stability and unique three-body orbital dynamics. The Linked Autonomous Interplanetary Satellite Orbit Navigation (LiAISON) technique is used to process the satellite-to-satellite tracking (SST) range measurements between a DRO satellite and another satellite in cislunar space to determine their absolute orbital states. The paper evaluates the navigation performances of the LiAISON, which are subject to dynamic model errors and satellite-borne clock errors. The clock models are presented, with a specific emphasis on modeling the non-Gaussian stochastic noise time series that are consistent with the clock instability. Comprehensive simulation results show that the SST system is observable. The DRO and Earth-orbit or lunar-orbit can obtain position accuracies of 100 m and several meters, respectively, and time synchronization accuracy is better than 100 ns. The Earth-Moon transfer orbit is less observable due to its long-orbital period that results in poor measurement geometry.