The refilling of the lunar wake is relatively well explained by the theory of 1-D plasma expansion into a vacuum; however, the field-aligned wake potential is not a directly measured quantity, and thus, a statistical analysis of wake potentials at high altitudes has not been previously performed. In this study, we obtain the wake potential by comparing the field-aligned electron distributions inside and outside of the lunar wake measured by the two probes of the Acceleration, Reconnection, Turbulence, and Electrodynamics of Moon's Interaction with the Sun (ARTEMIS) mission. The derived potentials from ARTEMIS data vary with solar wind electron temperature and bulk flow velocity as the theory predicts. We also expand the 1-D plasma theory to 2-D in the plane of the interplanetary magnetic field and the solar wind velocity to examine how a tilted interplanetary magnetic field affects the wake potential structure. As the expansion time for the two sides of the wake differs, a wake potential asymmetry is developed in our model. This asymmetry is confirmed by the data-derived wake potentials. Moreover, ambipolar electric fields are obtained from both the modeled and data-derived wake potentials and show good agreement. Lastly, we examine the effects of the solar wind strahl-electron population on the wake potential structure, which appears to cause a net potential difference across the lunar shadow. This may imply that the disturbance of the wake plasma expansion extends farther outside the wake than previous plasma-expansion theories have predicted.