Charting the Lyman-

Context. The escape of Lyman-α photons at redshifts greater than two is an ongoing subject of study and an important quantity to further understanding of Lyman-α emitters (LAEs), the transmission of Lyman-α photons through the interstellar medium and intergalactic medium, and the impact these LAEs have on cosmic reionisation. Aims. This study aims to assess the Lyman-α escape fraction, fesc, Lyα, over the redshift range 2.9 < z < 6.7, focusing on Very Large Telescope/Multi Unit Spectroscopic Explorer (VLT/MUSE) selected, gravitationally lensed, intrinsically faint LAEs. These galaxies are of particular interest as the potential drivers of cosmic reionisation. Methods. We assessed fesc, Lyα in two ways: through an individual study of 96 LAEs behind the A2744 lensing cluster, with James Webb Space Telescope/Near-Infrared Camera (JWST/NIRCam) and HST data, and through a study of the global evolution of fesc, Lyα using the state-of-the-art luminosity functions for LAEs and the UV-selected ‘parent’ population (dust-corrected). We compared these studies to those in the literature based on brighter samples. Results. We find a negligible redshift evolution of fesc, Lyα for our individual galaxies; it is likely that it was washed out by significant intrinsic scatter. We observed a more significant evolution towards higher escape fractions with decreasing UV magnitude and fit this relation. When comparing the two luminosity functions to derive fesc, Lyα in a global sense, we saw agreement with previous literature when integrating the luminosity functions to a bright limit. However, when integrating using a faint limit equivalent to the observational limits of our samples, we observed enhanced values of fesc, Lyα, particularly around z ∼ 6, where fesc, Lyα becomes consistent with 100% escape. This indicates for the faint regimes we sampled that galaxies towards reionisation tend to allow very large fractions of Lyman-α photons to escape. We interpret this as evidence of a lack of any significant dust in these populations; our sample is likely dominated by young, highly star-forming chemically unevolved galaxies. Finally, we assessed the contribution of the LAE population to reionisation using our latest values for fesc, Lyα and the LAE luminosity density. The dependence on the escape fraction of Lyman continuum photons is strong, but for values similar to those observed recently in z ∼ 3 LAEs and high-redshift analogues, LAEs could provide all the ionising emissivity necessary for reionisation.