Probably from the alternate of erchomai; unrestrained (to go at pleasure), i.e. (as a citizen) not a slave (whether freeborn or manumitted), or (genitive case) exempt (from obligation or liability) -- free (man, woman), at liberty.
see GREEK erchomai
ἐλευθέρα (eleuthera) − 3 Occurrences
ἐλευθέρας (eleutheras) − 4 Occurrences
ἐλεύθεροί (eleutheroi) − 6 Occurrences
ἐλεύθερος (eleutheros) − 8 Occurrences
ἐλευθέρους (eleutherous) − 1 Occurrence
ἐλευθέρων (eleutherōn) − 1 Occurrence