For those familiar with the solutrian migration theory the Lumbee population might represent a population of people descended from original ice-age migrants who made it here from Europe around 50,000 years ago. Many early European explorers noted indigenous people along the east coast who had blue eyes and some with blond and red hair. The red hair and blue eyes also played a part in the god legends of the Aztecs.
Sounds like a lot of hooey. Even if some visitors did report Indians with white ancestry (a lot of which are hoaxes, like the fairy-tale of the Welsh-speaking Indian tribe propagated by Morgan Jones) these all came well after European explorers had reached North American shores, and hence require no explanation other than a sailor's layover.