I shot a buck last year with the same issue. While it was down I noticed a discharge from it's nose like a little kid with a bad cold. I gutted it and noticed the lungs were exactly as you described and they were adhered to the inside of the chest cavity with those web like strands. I skinned it out and cleaned the carcass well and hung it over night but it still had an off putting smell in the cavity. The next day I called my local GC office and the warden called me back and was interested in checing it out. He thought pneumonia also but also offered to issue me a new tag. I asked him what he would do if it was his deer and he said he would take the the new tag. He did check with a biologist and the biologist agreed it was pneumonia.
I was glad I got a replacement tag because I don't think I could have enjoyed eating that deer, even if the meat was fine, after seeing and smelling it.
You may want to report it and see what the warden suggests.