Abstract Lyα emission from galaxies can be used to trace neutral hydrogen in the epoch of reionization, however, there is a degeneracy between the attenuation of Lyα in the intergalactic medium (IGM) and the line profile emitted by the galaxy. Large shifts of Lyα redward of systemic due to scattering in the interstellar medium can boost Lyα transmission in the IGM during reionization. The relationship between the Lyα velocity offset from systemic and other galaxy properties is not well established at high redshift or low luminosities, due to the difficulty of observing emission lines which trace the systemic redshift. Rest-frame optical spectroscopy with JWST/NIRSpec has opened a new window into understanding Lyα at z > 3. We present a sample of 12 UV-faint galaxies (−20 ≲ M _UV ≲ −16) at 3 ≲ z ≲ 6, with Lyα velocity offsets, Δv _Lyα , measured from the Very Large Telescope/MUSE and JWST/NIRSpec from the GLASS-JWST Early Release Program. We find a median Δv _Lyα of 205 km s⁻¹ and standard deviation of 75 km s⁻¹, compared to 320 and 170 km s⁻¹, respectively, for M _UV < −20 galaxies in the literature. Our new sample demonstrates the previously observed trend of decreasing Lyα velocity offset with decreasing UV luminosity and optical line velocity dispersion, which extends to M _UV ≳ −20, consistent with a picture where the Lyα profile is shaped by gas close to the systemic redshift. Our results imply that during reionization Lyα from UV-faint galaxies will be preferentially attenuated, but that detecting Lyα with low Δv _Lyα can be an indicator of large ionized bubbles.