You need to go out after dark with a torch and check what's there - it sounds like the sort of thing earwigs would do. Alternatively, put an upturned pot full of straw (yea, I know, who's got straw these days) or shredded up paper on a bamboo cane next to the lilies - if its earwigs, they like to hide in places like this during the day, so if you tip it out in the morning, you'll see if there are earwigs about.

I found a mighty big green caterpillar on mine which had chomped it's way through two flowers.