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The time frame in which hydrogen reionization occurred is highly uncertain, but can be constrained by observations of Lyman-alpha (Lya) emission from distant sources. Neutral hydrogen in the intergalactic medium (IGM) attenuates Lya photons emitted by galaxies. As reionization progressed the IGM opacity decreased, increasing Lya visibility. The galaxy Lya luminosity function (LF) is thus a useful tool to constrain the timeline of reionization. In this work, we model the Lya LF as a function of redshift, z = 5 10, and average IGM neutral hydrogen fraction, xH?. We combine the Lya luminosity probability distribution obtained from inhomogeneous reionization simulations with a model for the UV LF to model the Lya LF. As the neutral fraction increases, the average number density of Lya emitting galaxies decreases, and are less luminous, though for xH? ? 0.4 there is only a small decrease in the Lya LF. We use our model to infer the IGM neutral fraction at z = 6.6, 7.0, and 7.3 from observed Lya LFs. We conclude that there is a significant increase in the neutral fraction with increasing redshift: = = - = = ? x z 6.6 0.08+ , x z 7.0 0.28 0.05 H 0.05 0.08 ? ( ) H? ( ) and = = - x z 7.3 0.83+ H 0.07 0.06 ? ( ) . We predict trends in the Lya luminosity density and Schechter parameters as a function of redshift and the neutral fraction. We find that the Lya luminosity density decreases as the universe becomes more neutral. Furthermore, as the neutral fraction increases, the faint-end slope of the Lya LF steepens, and the characteristic Lya luminosity shifts to lower values; hence, we conclude that the evolving shape of the Lya LF not just its integral is an important tool to study reionization.