  Lithium niobate (LiNbO$_3$, LN) is a ferroelectric crystal of interest for
integrated photonics owing to its large second-order optical nonlinearity and
the ability to impart periodic poling via an external electric field. However,
on-chip device performance based on thin-film lithium niobate (TFLN) is
presently limited by optical loss arising from corrugations between poled
regions and sidewall surface roughness. Atomic layer etching (ALE) could
potentially smooth these features and thereby increase photonic performance,
but no ALE process has been reported for LN. Here, we report a directional ALE
process for $x$-cut MgO-doped LN using sequential exposures of H$_2$ and
SF$_6$/Ar plasmas. We observe etch rates up to $1.01 \pm 0.05$ nm/cycle with a
synergy of $94$%. We also demonstrate ALE can be achieved with SF$_6$/O$_2$ or
Cl$_2$/BCl$_3$ plasma exposures in place of the SF$_6$/Ar plasma step with
synergies above $90$%. When combined with a wet post-process to remove
redeposited compounds, the process yields a 50% decrease in surface roughness.
With additional optimization to reduce the quantity of redeposited compounds,
these processes could be used to smoothen surfaces of TFLN waveguides etched by
physical Ar$^+$ milling, thereby increasing the performance of TFLN
nanophotonic devices or enabling new integrated photonic capabilities.
