The Moon and its surrounding cislunar space have numerous unknowns, uncertainties, or partially charted phenomena that need to be investigated to determine the extent to which they affect cislunar communication. These include temperature fluctuations, spacecraft distance and velocity dynamics, surface roughness, and the diversity of propagation mechanisms. To develop robust and dynamically operative Cislunar space networks (CSNs), we need to analyze the communication system by incorporating inclusive models that account for the wide range of possible propagation environments and noise characteristics. In this paper, we consider that the communication signal can be subjected to both Gaussian and non-Gaussian noise, but also to different fading conditions. First, we analyze the communication link by showing the relationship between the brightness temperatures of the Moon and the equivalent noise temperature at the receiver of the Lunar Gateway. We propose to analyze the ergodic capacity and the outage probability, as they are essential metrics for the development of reliable communication. In particular, we model the noise with the additive symmetric alpha-stable distribution, which allows a generic analysis for Gaussian and non-Gaussian signal characteristics. Then, we present the closed-form bounds for the ergodic capacity and the outage probability. Finally, the results show the theoretically and operationally achievable performance bounds for the cislunar communication. To give insight into further designs, we also provide our results with comprehensive system settings that include mission objectives as well as orbital and system dynamics.