Voles. They get right thru the rabbit fence and get the small lily offset stems first and when they're gone, they go on to the bigger ones, ripping the bark away to get at the lower leaf stems. They often will chew off a whole stem to fall it so the can gain access to all the leaf stems.
Instead of using rabbit fence as you show, use 1/2 inch hardware cloth surounded at the base with either wood chips or gravel.Voles are devasting to lilies.

Thank you interspecific. You can not imagine the problems I have had trying to grow lilies. I love them so, but I can`t deal with the wildlife devastation. I appreciate the time you took to answer me. Lesley