My lungs always seemed to be the most limiting thing for my performance. And it stands to reason since they get CO2 out and O2 into your bloodstream so the muscles can use it.
It's been a 10 year process, but I don't feel as limited by my lungs as I once did. Though they are still probably the thing that limits me most. It's just that I've trained my legs and the rest of me to deal with their limitations. But.... it takes time.
Deep breathes anytime you think about breathing on or off the bike. If you cough after taking several deep breaths, then you need to work on that. I too used to cough after a really deep breath or two. Now I can breath deep and fast for a long time without wanting or needing to cough.
I read that pro cyclist have a very fast respiration rate on the bike. Somewhere on the order of 60 breathes per minute. But I only saw that once. Don't know if I was mistaken nor have I searched further for more info. Anyone else know about that?