I would just dig them now and immediately plant them in the new location, rather than storing them over the winter. The pips are small, and can dehydrate easily, so I think they'd be better off in the ground.
If I'm not mistaken, Lily of the Valley needs a period of cold, in order to bloom. If they aren't in the ground during the winter, you'll have to provide a period of cold storage indoors before you replant the pips in the spring.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams