I don’t talk about this much, for a lot of reasons, but I have fibromyalgia, a pretty severe case, and have had it for a long time. Usually, it is an annoyance, but it is occasionally debilitating and a couple of times, a hospital stay has been necessary. Most people I know are not aware of it at all, which I think is part of what makes it invisible, we often tend not to talk about our conditions.
This is probably not the most well-considered answer, but for me, putting in a character who had fibro really does feel like it would come off as Mary Sue-ish. Upon consideration, I think that is probably bad reasoning. I will have to give it some thought.
I don’t know much about Lyme Disease but it would be interesting to have a character who had something like that. Lord knows a lot of readers suffer from invisible conditions.