According to the closed captions, it's Deak Clancy's hunting shack, but it's hard to hear.
As for Lucy Mae, she never gets mentioned again, but there were other Lucys:
In 'Route 7-11', Dewey Stovall says he gambled "every cent Lucy and I ever owned." I'm guessing that was his wife.
In 'The Legacy', Boss calls old flame Lucinda Meadows "Lucy Ducy" a couple of times.
In 'Undercover Dukes Part Two', a lady called Lucy brings a present to Uncle Jesse's birthday. She obviously knows the Dukes, but I don't think she appears (or is even mentioned) in any other episodes.