Twenty-five years ago, I made a Christmas tree skirt with green/red plaid taffeta and red twill on other side, with expensive delicate white lace. I over watered the tree this year and the skirt got wet.
You can try Rit Dye/Color Remover. Take a look at this site: www.ritdye.com/
Follow the Rit instructions EXCEPT, only dip the lace part with the color that bled onto the lace, NOT the whole thing. Good luck.
It would be a lot of work, but you could also take the skirt apart, bleach the lace, then put the skirt back together.
Brightly colored sections on a dress can bleed onto the surrounding lighter parts. This page is about what to do when a dress bled on itself in wash.
Certain fabrics and dyes tend to bleed in the wash. Having this happen to a quilt that you spent hours making or to an heirloom one is saddening.