Try using a very potent anti-fungal/anti-parasitic oil or lotion on your lips at least 2-3 times daily.
Be absolutely certain to rub it in very well. Be consistent with any debridement (removal of dead tissue).
Continue with this approach until the symptoms are gone then continue for 2 weeks longer.
If it comes back, repeat the process as long as needed until it is completely gone.
This condition is typically caused by a mite and secondary fungal infection.
I used a potent anti-fungal oil and applied it three times daily and it was completely gone in 3-4 weeks. I rubbed it in very well and often would apply the oil, rubbing it in vigorously to de-bride, wipe this off, then reapply.
Internal: take organic raw apple cider vinegar (if you can), alkaline diet (eat more raw foods) and consume many anti-fungal foods and beverages (e.g, take oregano drops/capsules, garlic, onion, probiotics, coconut oil, etc..).
PS: Some suggestions which have worked for many:
Fung-e-clenz (wild oregano, wild sage, wild cumin, wild myrtle essential oils in a base of olive oil)
Zolvex - oregano, black seed, bay oils
Oreganol - regular or super strength (wild oregano essential oil in olive oil)
Etc.... (e.g., look for very potent anti fungal essential oils and mix with mite killers in a carrier oil)