Please tell me how long it takes for periodontal disease to heal?

What Stage?: This entirely depends on the severity of your periodontal disease. In the 1st stages, it can heal within the week. In the advances stages, it is too far along to heal = you will lose teeth due to bone loss.

May be chronic: After the first phase of treatment (a deep cleaning) the dentist should recheck you about five weeks later and there should be an idea then about how you are doing. But periodontitis needs to be maintained or it will come back.

Life long process: By definition, if you have periodontal disease there has been some level of bone attachment loss, this will likely not come back so you can not really heal completely. The treatment goal is to decrease the space between your gums and your teeth (pockets), as your gums heal, they shrink allowing better cleansability but any lost bone does not grow back as the phrase healing may imply.