Doctor says that the lower lobe of my right lung is damaged and it is the cause for the blood in sputum. Is this a good diagnosis?

No. It is important to find out the cause for blood in the sputum, especially is it is a repeated problem. The possible causes can be mild and once-only (certain viruses) but can also be an important sign of serious disease. Often a chest ct scan or other tests are needed to figure out the cause. If you are told it is due to "lung damage", find out what they mean and why it happened.