Lycra can be appliqued. We used to applique stars, etc, onto leotards and costume. It doesn't really ravel, but it makes LINT when you sew it. You can fuse it down with a low temp fusible. I would also satin stitch the applique down.
Daughter used to skate and dance and I've made costumes. If you have bought dance costumes, some used to have a sleazy satin. I'd be more leary of that.

You might try cutting the shape of 'legs' out of stiff interfacing (kinda like the cardboard placed in stockings?), put them in the tights, and then applique them on top of a pieced quilt. That would be the only thing I'd try. I agree with the others - it will probably be a tough job.