We present a large spectroscopic campaign with Keck/Multi-Object Spectrometer for InfraRed Exploration (MOSFIRE) targeting Ly emission (Ly ) from intrinsically faint Lyman-break galaxies (LBGs) behind 12 efficient galaxy cluster lenses. Gravitational lensing allows us to probe the more abundant faint galaxy population to sensitive Ly equivalent-width limits. During the campaign, we targeted 70 LBG candidates with the MOSFIRE Y band, selected photometrically to cover Ly over the range 7 < z < 8.2. We detect signal-to-noise ratio > 5 emission lines in two of these galaxies and find that they are likely Ly at z = 7.148 0.001 and z = 7.161 0.001. We present new lens models for four of the galaxy clusters, using our previously published lens models for the remaining clusters to determine the magnification factors for the source galaxies. Using a Bayesian framework that employs large-scale reionization simulations of the intergalactic medium (IGM) as well as realistic properties of the interstellar medium and circumgalactic medium, we infer the volume-averaged neutral hydrogen fraction, , in the IGM during reionization to be at z = 7.6 0.6. Our result is consistent with a late and rapid reionization scenario inferred by Planck.