I've dyed cotton tights before, and found that you have to thoroughly rinse them and then re-dye them till you get the color you want.  They really need to be rinsed well because the color can still rub out on you when you sweat.

I've dyed mylon tights, but a few years ago.  I had to get a special synthetic fabric dye for them (Woolworth's carries this stuff.), and it took several cycles before the dye took, and then several more before I got the color I wanted.

As for lycra, I tried to dye a white thong-backed leotard once, and it was a mess.  I used RIT dye that you buy in most stores.  The fabric looked like some of the fibers took the dye, but other fibers stayed white.  When you stretched it, it looked part purple and part white.  When I took it off, I looked part purple!

There must be some special dye for lycra, and I've seen lots of lycra web-sites, including one from the people who invented lycra (they can probably tell you what's best).  However, there are a lot of lycra web-sites, including a newsgroup-alt.lycra site, where you'd probably find people who dye lycra a lot (besides doing other things with it!).

There are too many places for dancewear where you can order what you want, so I've given up dyeing!  But GOOD LUCK!  balletboy