There's a human settlement at the north pole of the moon large enough to sustain expansion outwards for say 100 km in all directions. Humans like to think in terms of four principal cardinal directions: north, south, east and west. That works fine on Earth since since civilization has had no desire to live at the poles. But that won't be the case on the Moon -- the poles will be prime real-estate. There, notions of north and east will have little meaning with respect to local terrain. If someone asked you "which way is north?" the direction you would point to on the horizon would depend on your relationship to the pole at that particular time. Not a useful system for providing directions to lost travelers.
A more pragmatic system for direction bearing would be in relation to the Earth, since it would be near the horizon and generally in the same direction at all times (taking a small circular path slightly above to slightly below the horizon throughout the year). But what then would be good colloquial "homesteader" names for the four cardinal directions with respect to it?
Toward Earth might sensibly be called "earthward". But what about in the opposite direction and the two orthogonal directions?