Glads, I don't know, but for lilies, don't cut them down.

After they bloom, deadhead them, but leave the stalks and leaves to store energy for next year. Once they turn brown, remove the dead foliage. I'd imagine you'd treat Glads the same way--they aren't hardy in my zone, though, so I don't grow them.

Leave the lily stem until they die back in late fall. You can deadhead the lily but cutting the pedicels off (the small flower stalks which holds the flower to the main stem) to avoid having the lily spent energy on producing seeds. But let the main flower stem stay. Continue to water and fertilize.

In late fall, after the stem is brown you can cut it back to the ground, but not before.