I've dyed towels before, Jo, but I think in this case, unless you want them dark brown (?), you'd have to strip them of their original colour first. Dylon do a machine dye, which is easy to use and they also do stuff for getting rid of the original colour, before you embark on the dyeing. Actually, I think lilac & purple would go quite well with stone & beige...
Anyway, good luck! (oh, it costs about �5 a pack & one pack would probably do a bathsheet, or equivalent, so not cheap!)