  Lyman-alpha (Ly$\alpha$) emission from galaxies can be used to trace neutral
hydrogen in the epoch of reionization, however, there is a degeneracy between
the attenuation of Ly$\alpha$ in the intergalactic medium (IGM) and the line
profile emitted from the galaxy. Large shifts of Ly$\alpha$ redward of systemic
due to scattering in the interstellar medium can boost Ly$\alpha$ transmission
in the IGM during reionization. The relationship between Ly$\alpha$ 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 systemic redshift. Rest-frame optical spectroscopy with
JWST/NIRSpec has opened a new window into understanding of Ly$\alpha$ at z>3.
We present a sample of 12 UV-faint galaxies ($-20 \lesssim$ MUV $\lesssim -16$)
at $3 \lesssim z \lesssim 6$, with Ly$\alpha$ velocity offsets, $\Delta
v_{\mathrm{Ly}\alpha}$, measured from VLT/MUSE and JWST/NIRSpec from the
GLASS-JWST Early Release Program. We find median $\Delta v_{\mathrm{Ly}\alpha}$
of 205 km s$^{-1}$ and standard deviation 75 km s$^{-1}$, compared to 320 and
170km s$^{-1}$ for MUV < -20 galaxies in the literature. Our new sample
demonstrates the previously observed trend of decreasing Ly$\alpha$ velocity
offset with decreasing UV luminosity and optical line velocity dispersion,
extends to MUV $\gtrsim$ -20, consistent with a picture where the Ly$\alpha$
profile is shaped by gas close to the systemic redshift. Our results imply that
during reionization Ly$\alpha$ from UV-faint galaxies will be preferentially
attenuated, but that detecting Ly$\alpha$ with low $\Delta
v_{\mathrm{Ly}\alpha}$ can be an indicator of large ionized bubbles.
