Different people cope with serious illnesses in different ways. Her way (that is learned from her family) is to shrug it off and laugh about it. In a way this works pretty well to cope with the pain. She just doesn't take it very serious, while it really is very serious. If she goes through the day with less pain this way it's a good thing for her.

You two seem different is this aspect. You are more serious, want to talk about things. While she jokes about it. You can't ask her to change of course. All you can do is be there for her, and be there for her in a way that fits her personality.

You should really ask her if she wants to talk about it. You can keep guessing about it, but that will just give you an headache. I don't think anything bad can come from asking her if she wants to talk about her lung disease.