  We report observation of sub-Doppler cooling of lithium using an
irregular-tetrahedral laser beam arrangement, which is produced by a
nanofabricated diffraction grating. We are able to capture 11(2) % of the
lithium atoms from a grating magneto-optical trap into $\Lambda$-enhanced $D_1$
gray molasses. The molasses cools the captured atoms to a radial temperature of
60(9) $\mu$K and an axial temperature of 23(3) $\mu$K. In contrast to results
from conventional counterpropagating beam configurations, we do not observe
cooling when our optical fields are detuned from Raman resonance. An optical
Bloch equation simulation of the cooling dynamics agrees with our data. Our
results show that grating magneto-optical traps can serve as a robust source of
cold atoms for tweezer-array and atom-chip experiments, even when the atomic
species is not amenable to sub-Doppler cooling in bright optical molasses.
