I found this book in an article about gay authors' favorite books, and this was mentioned multiple times. The title is like the book, both in earnest and in jest. The two "ladies" in question are Christina Goering and Frieda Copperfield, who both are trying to discover themselves in different but absurd ways. Goering is an heiress who moves out of her mansion into a desolate shack on an island, allows her house to be inhabited by gold-digging hangers-on, and finds herself going home with a series of disreputable men. Meanwhile, Copperfield goes to Panama with her husband, only to abandon him in order to take up with a teenage prostitute and the middle-aged proprietoress of a run-down hotel. For being published in 1943, it's quite frank about bodies and sexuality. It's oddly compelling and amusing, though I wasn't entirely sure what to make of it at times.