Per one other comment here, Lauren is implied to be lesbian in this film. She pointedly scorns Doris for being "so terribly normal". Censorship at the time prohibited any open portrayals of any gay people so Lauren had to be sort of ambiguous.
This is such an interesting scene. Bacall and Douglas knew each other from NY and were friends. Douglas didn’t relate to Day. Doris Day was a movie neophyte and thought of, by trained actors, as only a band singer. Yet, all three stars were in transition.
It's very subtle; in the era this movie was made it couldn't be overt, but Bacall's character was a closeted lesbian. It seems to increase Douglas's character's attraction to her. He thinks there's something deeply sophisticated about her.
