I am borrowing pix from a couple of bulb and perennial catalog websites to see if we can get to the bottom of this. (Thank you Van Bourgondien and invasive.org.) See if they are tiger lilies–tall, dark orange, late summer. If this (TIGER.jpg) looks like your flowers, I’d leave them in the ground, mark off the area so it doesn’t get mowed anymore, and cross all fingers that they can manage to resprout some foliage to feed themselves. Lilies are best dug in early fall, I think, once they’ve had the chance to grow leaves and nourish themselves all summer long and the foliage has begun to wither on its own. If they are daylilies (DAYLILY.jpg), which have more long, strappy foliage arching up from ground level, then no worry no matter what has been done. They are like steel. You can leave them as is or move them now (the supposed "ideal" time is after summer bloom, in early fall, but they are too rugged to really care when).