Based on the candidate architectures of the libration point satellite navigation system proposed in our previous work, a navigation performance study is conducted in this paper to verify the cislunar navigation ability of the proposed system. Using scalar satellite-to-satellite range measurement between the user and libration point navigation satellites, a virtual lunar exploration mission scenario is developed to verify the navigation performance of the candidate Earth-Moon L1,2,4,5 four-satellite constellations. The simulation results indicate that the libration point satellite navigation system is available for cislunar navigation and the navigation accuracy of a few tens of metres can be achieved for both the trans-lunar cruise and lunar orbit phase. Besides that, it is also found that the navigation accuracy of the libration point satellite navigation system is sensitive to the orbit of the L1 satellite. Once the L1 navigation satellite is located in the Halo orbit or vertical Lyapunov orbit, the proposed system can present a better navigation performance in cislunar space.