Yes this lip problem can lead to social anxiety disorder because you will be thinking that people are watching your lips all the time and you will feel self consious about it and will be afraid to be seen in public.
It may cause all kinds of other mental problems too because of it, such as low or no self esteem, depression, you may feel as if you are useless, hopeless, inferior to others, etc. Those feelings lead to physical problems too.
This thing is a total life wrecker!! It wrecked mine totally.