You are absolutely right - the red lily beetle feeds on true lilies, not daylilies. I was so focused on the damaged petals in the photos and read lilies and it stuck with me - I should have examined the foliage in the background (it does appear to be a daylily to me, also).
The only common daylily pests that I am aware of are aphids, thrips, slugs and spider mites. The description of tiny, flying things in post #10 makes me think of thrips but the damage ??? Also, I see what may be honeydew on a leaf in the last photo which makes me think of aphids but I don't see any aphids in the photos. What is your feeling?