Answer: If you are speaking of daylilies (Hemerocallis), you can move them just about anytime, since they're extrememly sturdy and hardy plants. Water them well the day before you dig them, and spend time preparing the new bed before you dig them. A cool, overcast day is the best for transplanting. If transplant day is warm and sunny, they'll just take a bit longer to recover. They probably will cease to bloom after transplant, since they'll be concentrating energy on forming new roots.
If you speak of orientals, asiatics, etc. (Lilium species and cultivars), they are a bit fussier. Early spring or in fall, after the foliage dies back, are the best times to transplant. Enjoy!
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