I'm so sorry your Lily has been struggling so much.
You are doing your very best by her and giving her all the chances to pull through.
Sadly despite our combined efforts with the vet things may not go the way we want to and when running out of options, the decision to let them go, as painful as it is, turns out to be the right thing to let them go with the dignity they have left when they are at the stage where their quality of life won't improve, quite the contrary. At least this is how I think and I have sadly experienced it too and know it's not an easy decision to come by.
I sincerely hope your Lily recovers and is able to find happiness and enjoy life.