Why do people get panic attacks? Do panic attacks mean that you have a lung problem?

Not usually. If you have a true panic attack it is not a lung problem but if you have a lung problem and can't breathe, you could certainly feel panic. So before it is assumed that the problem is a panic attack, it is important for a doctor to do an examination to make sure there is not a lung or heart problem.
No. Why would you think a panic attack is a lung problem? Call you doctor.