The time frame in which reionization occurred during the Epoch of Reionization is highly uncertain. Fortunately, the galaxy Lyman-alpha (Lyα) luminosity function (LF) is a useful tool to help constrain the timeline of reionization. In this work, we model the Lyα LF as a function of redshift, z = 5-10 and average IGM neutral hydrogen fractions, xHI which includes realistic simulations for reionization. Our approach accounts for the changes in density of the neutral atomic hydrogen in the intergalactic medium (IGM) over cosmic time, an important effect because that hydrogen attenuates Lyα photons emitted by galaxies, changing the Lyα galaxy detection fraction as a function of redshift. We combine outputs of the Lyα luminosity probability distribution obtained from inhomogeneous simulations of reionization with an existing model for the UV LF to model the Lya LF. We predict that for a mostly ionized IGM, there is a small change in the number density of Lyα emitting galaxies detected, but as the neutral fraction increases, xHI≳ 0.4, the number density of Lyα emitting galaxies decreases and they are less luminous. We use our model to infer the posterior probability distribution of the neutral fraction at z = 6.6, 7.0, 7.3, given the observed Lyα LFs. We conclude that there is a significant increase in the neutral fraction with increasing redshift, consistent with a more neutral IGM. We also examine trends in the Lyα luminosity density and Schechter parameters as a function of redshift (over z = 5-10) and the neutral fraction. We find that the Lyα luminosity density decreases overall as the universe becomes more neutral. Furthermore, as the neutral fraction increases, we predict the faint-end slope of the Lyα LF steepens and the characteristic Lyα luminosity shifts to lower values, concluding that the evolving shape of the Lyα LF — not just its normalization — is an important tool to study reionization. The SAO REU program is funded in part by the National Science Foundation REU and Department of Defense ASSURE programs under NSF Grant no. AST-1852268, and by the Smithsonian Institution.