Dark horizontal line across my bottom lip and also a little bit on the top lip, how can I get rid of it ? (photos)

This can be improved with peels and skin lightening, but this is a genetic condition that typically cannot be reversed and is often seen in darker skin patients.  Sun protection is necessary to prevent further darkening.  Best, Dr. Emer.

You are describing melasma which is sun related and can be best avoided by sunscreen and the discontinuation of all photosensitizing medication.  Topical bleaching creams and retain-A combined with chemical peels will help remove this pigmentation.  Cosmelan is great especially when it is on many areas of the face.  Best, Dr. Green