Likely, what would happen is the dug and shipped lily would soon die back, bulb still intact, and come up next year. But it would grow to a much small size than previous. From then on it would grow normally. If the receiver is good with that, then I'd say okay. The correct genetics will always be there, but the plant has been through a lot of trauma.
Digging and transplanting growing lilies from one garden to another (your own or a neighbor's - no shipping involved) is more doable, but still will have noticeable, but more acceptable consequences.
Martagons may be the exception. Eugene Fox says in his book that a good time to transplant martagons is after flowering. This, of course, would not include shipping though. The idea is that transplanting in the active bulb and root growth stage (not top growth) will suppress the sulking tendency of the species in the ensuing season. Thus, there is no tendency to spend the first full growing season completely underground without sending up a shoot. Top growth in the first season is virtually assured.
I have to say, this seems to be true. For two years I had transplanted Claude Shride martagon bulbs into pots in the fall after tops died back. I wanted to sell them at our NARGS plant sale. All three times the bulbs did not send up shoots the first year, but did the second. Last year I transplanted in August (later than Fox's suggestion) while the top was still healthy looking. Subsequent growth is still abbreviated, but the result seems to be telling: pics taken today.
Plant sale is Saturday.
N.B. No pulling of the old stalk this time!