Not natural, but after years of trying to heal them with things that dry them out and make them very painful, I now use Blisteze (or Blistex) Daily lip conditioner. It comes in a little pot, and I use a clean finger and do application over my cold sore, then another clean finger and cover the rest of my lips. I find it keeps the superficial layer hydrated so none of that unpleasant throbbing, and the healing goes on underneath.
I have several friends who have tried it on my recommendation and have been very pleased!
Vicki x