What is the natural color of your lips? How old are you? Are you in the sun alot?
I think that since this has been going on for a year you should see a Dermatologist. Some oral cancers can start with a change in color like that. I am not trying to alarm you. It could be something more simple but I tend to stay on the safe side.
If it is not something serious then the Dermatologist can treat it or get you something that could help it.
I would hate to tell you to do something and make it worse. I think it really needs to be seen to be able to give a treatment protocol,
You can find more information here:
I wish you the best,