A pre-employment physical will likely ask if you have ever been treated for a whole list of things; answer truthfully. Plan to have proof of treatment and cure and be willing to provide a release of this information from your doctor if required. It is not likely to be a big issue except where TB test is required by law - like in schools, etc. Your local public health department and the HR representative of your employer will have knowledge of this issue.
If the lung damage limits your work conditions or duties (such as not work around chemical vapors, ...), this would need to be listed as needing disability accomodations but would not disqualify you from jobs whose physical requirements you meet. You obviously would not apply for jobs which you are physically unable to perform. Plan to have proof of accomodations or limitations required by physician's orders available and be willing to provide a release. Let HR walk you through this; they must protect your privacy rights. If you require no disability accomodations, just handle it with the physical like all other medical records. There are significant protections for your privacy in medical records and treatment. No one you work with will need to know of this history.
For the very best advice based on your specific health situation, speak with an attorney with a specialty in employment (not immigration) law about your rights and responsibilities. Since you appear to be concerned, the cost of a consultation could be justified for your peace of mind. If you are at a US university, the job placement office or student services/disability advocacy office may also have some information; you would need to speak with a high level administrator - not one of the support staff.
Don't worry. It is not a big problem as long as you are cured. Actually, if you have been in a US university setting as a student, you have been through one of the harder health screening processes that I have personally experienced.