To be honest, I am really not sure what you have. There are conditions which produce lip freckles, but these aren't usually associated with loss of color. The converse is true as well (loss of color doesn't come with freckles.) I think your dermatologist is similarly perplexed, which is why a biopsy is being recommended. A small biopsy (perhaps 2 mm) is not likely to leave much of a visible scar. I suspect the biopsy will be done on a freckle, though perhaps a second on on a pale, unfreckled area may be of value too. Hopefully, the test or tests will shed light on the nature of your problem, and possibly point to a modes of treatment not yet tried.
Best.
Dr. Rockoff