LFUCG = Lexington-Fayette Urban County Government. Lexington merged with Fayette county several years ago, and that's honestly the best name/acronym anybody could come up with, apparently, so expect to see it on everything. I believe the Division of Parks and Recreation gives out individual permits, so that's the approval you see.
And welcome to Lexington. I've lived there a while (although temporarily relocated), but I'm new to caching, so I'm not all that familiar with the approval process. The Parks & Rec site is here, and you can find more relevant information courtesy of Geocky here.
BTW, first post!
