Laura, since your first post, I've been looking on the internet to see what I could figure out. The only time I ever had the circular holes in anything like you have it turned out to be a spider. That was in siberian irises.
I did read on the internet where larvae of some beetles make circular holes, and that may be what that thing is you're picturing.
I just don't know, and I think we need to know. Could you maybe contact one of the lily growers and see what they might think is doing it?