This study presents an autonomous orbit determination system based on crosslink radiometric measurements applied to a future lunar CubeSat mission to clearly highlight its advantages with respect to existing ground-based navigation strategies. This work is based on the Linked Autonomous Interplanetary Satellite Orbit Navigation (LiAISON) method which provides an autonomous navigation solution solely using satellite-to-satellite measurements, such as range and/or range-rate, to estimate absolute spacecraft states when at least one of the involved spacecraft has an orbit with a unique size, shape, and orientation. The lunar vicinity is a perfect candidate for this type of application due to the asymmetrical gravity field: the selected lunar mission, an Earth-Moon L2(EML2) Halo orbiter, has an inter-satellite link between a lunar elliptical frozen orbiter. Simulation results show that, even in case of high-measurement errors (in the order of 100 m, 1σ), the navigation filter estimates the true states of spacecraft at EML2 with an error in the order of 500 m for position, and 2 mm/s for velocity, respectively and the elliptical lunar frozen orbiter states can be estimated in the order of 100 m for position and 1 cm/s for velocity, respectively. This study shows that range-only measurements provide better state estimation than range-rate-only measurements for this specific situation. Different bias handling strategies are also investigated. It has been found that even a less accurate ranging method, such as data-aided ranging, provides a sufficient orbit determination solution. This would simplify the communication system design for the selected CubeSat mission. The most observable states are found to be position states of the lunar orbiter via the observability analysis. In addition, the best tracking windows are also investigated for the selected mission scenario.