  Faint galaxies are theorised to have played a major role in reionising the
Universe. Their properties as well as the Lyman-{\alpha} emitter fraction,
could provide useful insight into this epoch. We use four galaxy clusters from
the Lensed Lyman-alpha MUSE Arcs Sample (LLAMAS) which also have deep HST
photometry to select a population of intrinsically faint Lyman Break Galaxies
(LBGs) and Lyman-alpha Emitters (LAEs). We study the interrelation of these two
populations, their properties, and the fraction of LBGs that display
Lyman-alpha emission. The use of lensing clusters allows us to access an
intrinsically faint population, the largest sample collected for this purpose:
263 LAEs and 972 LBGs between redshifts of 2.9 and 6.7, Lyman-alpha
luminosities between 39.5 < log(L)(erg/s) < 42 and absolute UV magnitudes
between -22 < M1500 < -12. We find a redshift evolution of the Lyman-alpha
emitter fraction in line with past results, with diminished values above z = 6,
taken to signify an increasingly neutral intervening IGM. Inspecting this
redshift evolution with different limits on Lyman-alpha equivalent width (EW)
and M1500 we find that the Lyman-alpha emitter fraction for the UV-brighter
half of our sample is higher than the fraction for the UV-fainter half, a
difference which increases at higher redshift. This is a surprising result and
can be interpreted as a population of low Lyman-alpha EW, UV-bright galaxies
situated in reionised bubbles. This result is especially interesting in the
context of similar, UV-bright, low Lyman-alpha EW objects recently detected
around the epoch of reionisation. We extend to intrinsically fainter objects
the previously observed trends of LAEs among LBGs as galaxies with high
star-formation rates and low dust content, as well as the strongest LAEs having
in general fainter UV magnitudes and steeper UV slopes.
