The best way to remove this would be direct excision with closure in such a way to leave a minimal scar. This is a fancy way of saying - moving making sure you scar is in a skin crease if possible or close to a normal anatomical structure after removal so that you scar is less noticeable. Lasers are generally not used and it is customary to send what was removed to a pathologist for analysis.
I Have a Medium Brown Birthmark on my Upper Lip. What's the Best Way to Get Rid of It?
Doctor Answers 3
Brown Pigmented Birthmark removal on lips and face
Lip birthmark removal
Best treatment for birthmark on lip
I know this answer will be unsatisfying, but there really is no way to tell without seeing you. There are many different kinds of brown spots and birthmarks. Some need to be excised and others can be treated by laser.
And sometimes, the exam is not always clear and a biopsy may be needed to determine the diagnosis and dictate what might be the best treatment.
See a Dermatologist.