I Have Developed Dark Pigments on my Upper Lip, Where I Had Laser Hair Removal. What Do I Do?

Post Laser Hyperpigmenation can be permanent but
it can also fade with time, you may want to speed up the fading process with
some HQ Cream (Hydroquinone). Please ask your medical aesthetician or plastic surgeon or recommendations on which cream would be best for you.

If you had laser hair removal several years ago, and it was uneventful, the darkening on your upper lip is from something else, not the laser hair removal procedure. I would suggest you find yourself a board-certified dermatologist or plastic surgeon and let them explain to you what the term melasma means and how the best way to treat this kind of pigment. Some have told people that they can cure melasma, when in fact, there is no known cure – but we can successfully treat it, whether with topicals, peels, or appropriate light sources. Sunscreen is by far, the most important part of the treatment and sun avoidance is also crucial. Your dermatologist will work with you to give you the best options and the best care, and understanding the nuances of this skin condition.

It is unlikely to be from the laser since it was so long ago, it could be melasma.  You need to see a good board certified dermatologist to get a good diagnosis and treatment plan.
We have lots of things to offer to treat hyperpigmentation. 

If the laser treatment was several years ago, it is quite unlikely that the hyperpigmentation would show up now.  Another possible cause of hyperpigmentation on the upper lip is melasma. 

Melasma is a common skin condition that causes tan to gray-brown patches on the face and develops mainly in women. It affects people of all ethnic groups, but particularly those with Fitzpatrick skin types IV–VI.

It's not known why melasma forms, but it is commonly associated with hormones and sun exposure.  That is why we often see it form during pregnancy and in women on oral contraceptives.  

The first line of treatment of melasma is sun avoidance and a combination of a fading cream and retinoids.  None of these treatments are approved to use during pregnancy, so if you are pregnant, I would suggest waiting until afterwards.