We report the 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 Λ-enhanced D₁ gray molasses. The molasses cools the captured atoms to a radial temperature of 60(9) μK and an axial temperature of 23(3) μK. 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.