Show Business: Liza, Gasping for Breath

She sprawls—giggling and gangly—in a Waldorf-Astoria suite, looking as out of place as a cheerleader at a debutante ball. Her shaggy haircut springs out from her head. Her nails are bitten to the quick, her black boot heels are run over. She sprays words and sounds. She is having a frantic kind of fun, like a kid rolling down a hill, dizzy and excited at the same time. But who cares? Certainly not Liza Minnelli.

She has wound up a successful engagement at the Waldorf's Empire Room, a knockout, nonstop show that had everybody—including Liza—gasping for breath. She opens at Puerto Rico's...