Is there a permanent solution to fine lines under eyes & nasolabial area? (Photo)

It appears that you have u see eye hollows or tear trough hollows from The one picture you have posted.
Without any other information such as age, what treatments you have tried, other photos- I can review briefly what your options would be

Hollowing under the eyes is a common concern and gives the appearance of looking tired.

There are solutions such as fillers/ last about a year , to facial fat transfer , which lasts years, lower eyelid blepharoplasty and laser skin resurfacing which toghtens the skin over the area

An examin and consultation would be best to discuss all options and treatments with expected outcomes.