Hi, I'm guessing you know this, but it is important to know if they are FIV,FeLV, or both. FIV kitties can live for a long time, and although they should be kept away from FIV negative cats, they should also nevercome in contact with FeLV cats. I just thought I should mention this, due to the wording of your question. If you are already aware of this, please disregard my warning!
As for L-Lysine, I have used it daily (for years) with wonderful results on two FIV positive felines, one of which tested positive as a kitten, and is now about eight years old. The down-side is that it can take some time to see results. Also, I suggest you give the highest recommended dosage and frequency in the beginning, and decrease it only after you've seen rock-solid results for quite a while. It does take some back and forth (with dosage and frequency) before finding your minimum management dosing level. In my case, it's easy to tell when my eight year old isn't getting a high enough dose because his eyes start running (probably from a herpes virus).
The main thing is to always make sure a FIV cat gets antibiotics when needed (infections, puncture wounds, abscessed tooth, etc.), since the immune system is compromised. The problem your cat is having with his/her mouth needs to be addressed by a Vet, which could solve your eating/not eating issues. Bad teeth can also cause heart problems, among other things...okay, I'm starting to ramble on now!
I hope this helps! Good luck!
