I had a very Dirty Lily Lightly myself, got her from a Garage sale for free two summers ago, here is what I did.
Take a damp Magic eraser for the surface dirt, and very VERY carefully wash the mane, don't let the water get to the roots. Lift up the dress, and do the same for the tail. Then style the mane as you see fit.
Personally I think she looks gorgeous with straw curls that are partial combed through. Soo much curls!!! Almost looked like the Merida dolls from Brave.