A cough is sometimes to referred to as "hacking", and in particular when it is induced by smoking. So for me "a hacker's lung" would be a lung that has been damage by a smoker's cough.
"You can't even sneak around without your hackers lung acting up".
Could also be expressed as "You cannot be dicreet seeing as your smoke damaged lung is giving you some trouble.
I think of "hacking" as that nagging dry cough that smokers have. So I would take it to mean that your cough gives you away when you're trying to be sneaky and quiet. At any rate, it should be hacker's (with an apostrophe).
I agree with your interpretation Lilly, but you need to insist on the fact that the lung is "acting up", which means that the cough has worsened (in acute phase). So it will be even more noticeable
Hope this helps a bit more (I can talk, I have a hacking lung too, from too many cigarettes