Well, Mr Bang is exaggerating. A lung puncture only causes a haemothorax if a vessel is sliced, which is often not the case. Most likely it's a plain pneumothorax, so a collapsed lung. And a pneumothorax is problematic if you don't get medical attention to reinflate the lung, because there may be permanent tissue damage if it stays collapsed. But each lung is insulated from each other in terms of expansion, so the other one isn't that much affected.
The body will respond by breathing faster to make up for the disabled lung, and how much faster the victim can breathe to compensate will depend on a lot of factors, including baseline physical performance, which in Jiyong's case is superathlete-level. He probably can't sustain strenuous exercise for long, but what we call his respiratory reserve is probably quite high. So yeah, he can still settle this in his favour if he fights with his brains, which we know he does.