gemma; my pond has various shade, meaning that as the sun moves east to west, each end of the pond gets shaded for a bit. The lilies still bloom, so I'm figuring I'm still getting them enough sunshine. I have my lilies all within 18" or so from the surface, either on a shelf or 'suspended' by trimmer twine. For the winter, I sink most to the bottom. And I do thin the plant herd sometimes, but it used to be mainly the floaters. Not this year as the fish are doing it for me. In the fall, I'll cut back the iris as I don't want them to get out of hand. I keep them either in the bog or in a pot. The 'specialty' iris I let go as they are not nearly as aggressive. I try to overwinter some of the plants so I don't have to totally go 'naked' once spring arrives. Like you, I have to wait until about the third week of May before I can get the more tender specimens into the pond.
My fish seem to go for the tender roots of the floaters (this year especially) and parrots feather when it moves from the stream into the pond proper. Then there's the monkey flower; it typically grows on the bank and as it gets heavy, sinks to the pond where it'll continue to grow--not this year as the fish have taken care of that, as well. Saved me the effort of having to trim it back (as I usually have to do). I also have some hornwort (oxygenator plant) growing and I can see they're keeping that trimmed. I guess what I'm saying is if you have enough plants, you won't miss some that get eaten and you'll still have the benefit of their growing/filtering.
I've not tried putting crates over any plants but would assume if there's enough room, that the lily should put up leaves, but it wouldn't be my first option. Give your fish something better/easier and I bet they'll leave your lilies alone. I haven't heard of too many on the forum that have had gf bother their lilies. Even my turtles are leaving them alone, so they too must be getting better snacks somewhere!
Michael