I found this link, it might help. I just transplanted some this week.

Here is a link that might be useful: daylilies

These are NOT daylillies. They are asiatic lillies. HUGE difference.

Opps sorry I misread. I also transplanted asiatic lilies while they were in bloom last week. they didnt even flinch!!!

Descending from best:

1) Fall
2) Spring (earlier the better)
3) Carefully at other times

Other Times:

Your bulb has been depleted by blooming so you need to be sure to preserve the stalk and leaves so they can build up the bulb.

Also, you need to dig a LARGE soil ball so that the roots are not harmed - otherwise your leaves "efforts" will go into growing new roots instead of building up the bulb.

Water well after planting to settle in the roots (like you would for any transplant).

That said hybrid asiatics are pretty tough, and not being as tall, are easier to move than the other lilies.

-Helen