Honestly, the best things you can do is to get rid of the fleas if she does have them (do watch her closely for any signs of problems with the flea meds, they CAN sometimes make them sick so when you give to her make sure you watch her closely), use a nice oatmeal based shampoo made for dogs (its really ont expensive and she's realy tiny anyway, don't need much), give her a healthy diet, brush her daily, and don't overbathe (she really doesn't need more than once a month unless somethign happens). If those things alone don't clear it up then it may be a medical issue and she would need to see a vet but it should help. Also someone mentioned those baby wipe types of cleaners you can get at the pet store, they wash the outside and dont get to the skin to cause dryness.

Also just for info sake a lot of the flea meds you can buy in the regular stores have caused LOTS of problems with dogs, even large ones. So I really really would suggest getting one your vet recommends even if it is more expensive. The others are insecticide, poison, and with Lily being so tiny, I would really hate to see something happen to her. I'm not trying to be a know it all honestly, but it's just really risky and I'd hate to see it cause her to be very sick or even die. I'm not making it up I promise.