Is the possessive "'s" also used, as in the following dialogue, for denoting original ownership/establishment?
A: Which bar did you go last night?
In part B, does the "s" mean that the bar was originally established/owned by someone called Lucky?
Probably, yes, but there's no guarantee. The founder of the bar may have simply liked the name. Perhaps he had a dog called Lucky and decided to name it after the dog. Unless you can find documentation showing the reasoning or actually ask the original owner, you would just have to guess.
The possessive 's is used in that way, though, yes.