Koi do eat plants, but some do & some don't - seems to be dependent on the animal. Feed them well and see how it goes.
Many/most people put their lilies into protective nets, though.
My Koi live with water lillies and others floating plants with no issues. Water lillies grow very fast.....the koi graze on algae and stuff clinging to the edge of the pond. I have had no issues both with light and heavy feeding.
It’s perfectly safe to grow plants with koi, but they might get eaten.
It really does depend on the koi. I’ve had koi that will eat every spec of green in the pond and yet my current group is letting me keep plants.
My small floats get eaten over time or end up dried on the rocks, but the lettuce, hyacinths, and lilies do well.