First time I hever heard Tex purr was when I was upset and on the phone. He was sitting in HIS box on the dining table next to me and ...rrrrrrrrrrrrrrrrr!!!! He knew I was worked up and was trying to help me!
I wish you could get that image out of your head too. I do not know if this would help you but when I get images of Claude having laying on the table at the vets when he had to be put down I try to force myself to remember when he would meow at me to pet him dry after a shower. If you can force your mind to think of the postive things you shared with Lilly maybe it will help.
I hope someone else has some other suggestions. I am sorry you are going through this.