One of the matches I found was a descendant of Curtis B. Lore, who would have been Grandma Potter's great-uncle. This cousin had done an enormous amount of research on the Lore family, as well as her other ancestors, and also wrote up much helpful documentation on how to use DNA tests for genealogy.
Her blog is http://dna-explained.com. It is well worth reading through. I am giving the short version in the next few posts.
Since the story involves the history of the Acadian people, which I did not know (a middle-school assignment to memorize the proem to Longfellow's "Evangeline" is as close as I ever got), a summary seems in order.
The earliest Lore in the Americas was Julien Laure dit Lamontagne (ca. 1653-1754), who arrived in Port Royal, Acadia, New France (now Annapolis Royal, Nova Scotia, Canada) somewhere between 1668 and 1670. He was probably a soldier at the time. The "dit(e)" name is a kind of formalized nickname of military origin (Julian "Mountain" Lore) typical of the Acadian settlers.
Acadia (which included the modern Canadian Maritimes, part of Quebec and the US State of Maine) was contested territory, with a long series of battles between the British, French and First Nations (this is, after all, a Canadian story at first).
By 1755, the British were in charge and had run out of patience with an Acadian insurgency, and decided to deport the entire population, without sorting out political neutrals. The citizens of Port Royal were among the first to be deported, including the children and grandchildren of Julien Lore. The initial deportations were to New England and New York, and several Lore families were put off the boat in New York (City) in December, 1755.
The British later reconsidered the wisdom of sending Acadians into such near-by territories, as the deportees did not stay put on the farms where they were indentured, but instead gathered into large, poor, French-speaking, Catholic communities in the Colonies. The Crown then turned to deporting Acadians to France and the Caribbean. This later wave of Acadians found passage to Louisiana, where their influence lives on in Cajun culture.
By 1768, the British decided to allow the surviving Acadians to leave the English-speaking colonies and migrate to Quebec. There was no point in returning to Nova Scotia, as the land had been given to English settlers, although a few of the old families did go back eventually.
The Lore family and close relations eventually settled half-way between Montreal and the New York/Vermont border in the village of l'Acadie. Grandma Potter's great-grandfather Antoine Lore was born and baptised there in 1805.