Louche, loose, lush...
..is there a connection, there?
Not a traceable one, no.
Thing Not To Be Today: louche. This word is French and means squinting. The word loose comes from the Old Norse lauss, free, and is perhaps related to the Old English lēas, and also to the word less. Lush meaning an alcoholic person appeared in English in the 1800s, but no one is really sure from where it came. There's a nice story that it comes from a London actors' drinking club called The City of Lushington. (Lush is an old name for strong beer.) It's tempting to say the club was named after the drink (the club did go in for silly names) and the alcoholic person was named after the club. But the proof just isn't quite there.
The word lush meaning strong beer may be the Irish Shelta word lush which means to eat and drink, or come from the German word for strong beer, Loschen.