Hi Greiners,
If you must dig then now, cut off all bloom stems on the daylilies, water well and dig within 48 hours of watering. For the lilies, cut off the flowers but leave the foilage to feed the bulbs for next years bloom, water well and dig after 48 hours as well. Watering this way will help to hydrate the plants and they should have less transplant shock. Keep in a part sun or even shady area after digging up to lessen stress. Replant where you want them in the fall. If they will need to overwinter, you can pot them up and just sink the pots in the ground for the winter. I've done it and it all worked out fine.
Hope this helps,
Newt
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.