I love Lush haircare...it took me a while to get used to it while it was getting the silicones out of my hair, but now my hair is healthier-looking than it's ever been. While I do have colored hair, I won't say my experience is all that meaningful for everyone since it is naturally dark brown and I've been dyeing it black for four years (not much to fade except maybe my roots!), but I've had no problems with Lush.
I know BIG is the, well, big (for lack of a better word) Lush shampoo in terms of popularity, but they have so many more awesome ones! I rotate between Trichomania, New!, and Cynthia Sylvia Stout, all with good results, and none have stripped or dulled my color. People use BIG sometimes specifically to strip color from their hair, so if you're concerned I would probably stay away from that particular one.