We only see Lucy for a couple of scenes, but it's a doozy. She bursts in on Polly and Mac's prison visit, claiming that she, not Polly, is Mac's wife. When she doubts that she's on the winning side of the battle, she claims to be pregnant.
Her willingness to lie in order to get what she wants makes her a chip off the old block. She is Sheriff Jackie Brown's daughter, after all. So we shouldn't be surprised at all that she doesn't have any qualms about immoral behavior.
While Polly pretends, at least, to uphold some kind of appearances (wanting to be treated as Mac's wife, for example), Lucy doesn't really worry about that kind of thing. In that way, she's more like Mac, while Polly is more like Peachum.