OP, ignore al the snobbery. It's different, and she'd have the choice of using the whole thing, or just Beau, or just Lilah.
I know Beau is a boys name because beau means handsome in French, but we are not French, and it looks like the first half of Beautiful to an English eye. You use Beau for her if you want! It looks and sounds really feminine. I always really cringed when friends used it for a boy. Conjures up images of a sickly, delicate, boy of yesteryear with a lace ruffle around his neck! 😂
PSA: It would be pronounced Bow Ly-la.