This should not be a problem Elizabeth.  While LLC's are non-natural entities they are populated by at least one natural person.  Your association should treat them the same as a natural individual, trust, corporation, or partnership.  It might be best to review your bylaws to see if they address the issue of non-natural owners and if not amend them to accommodate such ownership.  One thing to consider is requiring a non-natural owner appoint one person as its representative for voting and another to consider is allowing any member of the LLC, trust, corporation or partnership to be a director or officer of the association if so designated by the entity and requiring any such person also be the individual authorized to vote. 

Good question.  Thanks for submitting it.