A friend, visiting from elsewhere, enlightened my to the delightful prospect of eating Day Lilly petals! They are incredibly crisp and bitable, with a melon flavor. Melon might not be the best descriptor, but it is the best I can think of.
A google search has found lots of pages with recipes galore, like this page.
For now, I think I will add them to salads. It’s amazing how a few flowers or petals make a salad so much more delightful, as well as appetizing to the Little-Bugs. Thanks to my friend for the new edible flower!