A friend of mine who is an amazing cyclist (she's insane...she has been riding for not even 2 years and has already covered something crazy like 8k miles just in 2010. She got her new road bike in April and just posted on FB that she's done 5k miles already--makes my 3300 or so seem lame) has lupus and had her thyroid removed years ago, so she is on thyroid replacement hormones for that.
She was telling me a while back that part of why she bikes is that it makes her feel better and keeps her lupus symptoms at bay. I don't think she has any lung issues, though. I'm asthmatic, so I know what a damper bad lung days can be on anything aerobic.
I would ask your doctor for confirmation, but my guess is that cycling would be good for your conditions. Aerobic stuff definitely will strengthen your lungs and the low-impact nature of cycling would be gentle to your joints, once you have acclimated to the new stresses of riding.