Not only is it not in Finishing the Hat, the title is not listed in either Banfield's Sondheim's Broadway Musicals or Horowitz's Sondheim on Music: Minor Details and Minor Decisions, both of which have song lists that include many cut songs.
There are a bunch of omissions from Sondheim's two books, including "Philadelphia" from Do I Hear a Waltz? (a surprising omission because it was performed out of town, and it's a neat lyric) and "Happy Endings," an early attempt at an opening number for Forum.
I rather suspect that "Crinoline" may have been abandoned before it was finished. In any case, "The Ladies Who Lunch" was written at least a few months before rehearsals started, even though they had trouble coming up with a title for it, which seems odd. But in Boston playbills, at least early ones, it was listed as "Drinking Song."