  At redshifts beyond $z \gtrsim 30$, the 21cm line from neutral hydrogen is
expected to be essentially the only viable probe of the 3D matter distribution.
The lunar far-side is an extremely appealing site for future radio arrays that
target this signal, as it is protected from terrestrial radio frequency
interference, and has no ionosphere to attenuate and absorb radio emission at
low frequencies (tens of MHz and below). We forecast the sensitivity of
low-frequency lunar radio arrays to the bispectrum of the 21cm brightness
temperature field, which can in turn be used to probe primordial
non-Gaussianity generated by particular early universe models. We account for
the loss of particular regions of Fourier space due to instrumental limitations
and systematic effects, and predict the sensitivity of different representative
array designs to local-type non-Gaussianity in the bispectrum, parametrised by
$f_{\rm NL}$. Under the most optimistic assumption of sample variance-limited
observations, we find that $\sigma(f_{\rm NL}) \lesssim 0.01$ could be achieved
for several broad redshift bins at $z \gtrsim 30$ if foregrounds can be removed
effectively. These values degrade to between $\sigma(f_{\rm NL}) \sim 0.03$ and
$0.7$ for $z=30$ to $z=170$ respectively when a large foreground wedge region
is excluded.
