Yes, well, here in my city at the university there are two doctors with a certain degree of specialty in LC. One of them is a pulmonalogist, the other a rheumatologist.
I think that makes sense given the variability of symptom presentation we all have, and joint problems or lung problems are pretty typical of LC, along with others, e.g. digestive issues.
Since you sound as though joint problems are your issue, i guess a rheumatologist makes sense. Again, hopefully it's a doctor who is familiar with and understanding of LC, specifically.
Autoimmunity, inflammation, dormant virus re-activiation are just some of the theories behind the mechanism(s) of LC, and it seems that the jury is still out on which one is responible, or, perhaps there are different mechanisms with different people.
Personally, I lean toward the involvement of UFO activity, but that's just my personal take--no NIH-funded studies as yet.
Best of luck!