Yes, the noun phrase ladies' club is the possessive form of the club for ladies. The possessive noun ladies' is the plural possessive form.

And Ladies of the Club was created in 1982.

The plural possessive form is the ladies' club.

Samuel Johnson was the founder of the Literary Club.

If "Ladies Club" is a group name:

Although the Ladies Club met, no decision was made.

If not (it is just an unnamed club for ladies):

Although the ladies' club met, no decision was made.