Maybe the luna / lalo are simply added to underscore or intensify the meaning? Plenty of languages have constructions that essentially give you the same information twice.
Or maybe it could make it more specific or local to the person? E.g.:
E iho ma kai: Head down seaward.
E iho i lalo: Go down (to some place literally below you like a lower floor).
These are just guesses; I guess I will see in further lessons if the hypothesis holds up. :)