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.