I'm pretty sure Lysine won't hurt her if you are able to find a way to get it into her and hopefully, it will help. I know that she may not have the Herpes virus at all but if she does, the Lysine works wonders in just a few days.
Do you think she would entertain the idea of tuna juice (the human variety) with half a capsule of Lysine mixed in. Does she ever eat the hairball malt paste that comes in the toothpaste like tube? You could mix some in there.
It sounds like she doesn't have much interest in food though but if you could even get a little bit into her at a time, it might help.
She is so lovely in those pics even though she is not feeling that well.
I hope you are able to find a way to help her over the weekend. Do you have a thermometer to take her temp?