The first documented betty lamps seem to have come with the colonists at Plymouth in the early 1600s. Apparently, Captain John Carver brought a Dutch betty lamp that he had purchased in Holland while the Puritans were living there before coming to the Americas. What he brought may have been a crusie rather than a true betty, but the two are intimately related, the betty having a single improvement over the crusies of Scotland and Ireland, or the cressets of the Channel Islands. None of these is particularly more sophisticated than the stone oil lamp found in Lasceaux (around 17,000 BC).
The hanging system for these lamps predates the (apparently) German improvement of an internal support for the wicking (any drops of the fat or oil dropped back in the reservoir instead of on the ground).