A translator may rebroadcast the signal of a LPFM station. There are several LPFM stations around the country that enjoy this arrangement. As far as I know, it is untested if the FCC will actually let the LPFM licensee also own a translator. On the surface it would seem that it would be prohibited, but that could be subject to the interpretation of the wording of the rules. There are a couple of possible loopholes. A good communications lawyer might make it fly.
The usual arrangement is for a separate group to be formed to own the translator(s). These people are not voting members of the LPFM Board, but nothing says they can't be friends with the LPFM people.