There seem to be multiple origins of the name. North Americans in Louisiana or Canada might trace back to the french origin (Julien Lord). Others might trace back to a Brit named Thomas Lord.
French descendants with the name "Lord" trace back to Julien Lord dit Lamontagne, who came from France to Canada on the royal ship Saint Sebastien leaving St. Rochelle and arriving in Nova Scotia (then Port Royale) in 1670.
The orthography of the name Laure-Lord varies with which register is used; it is difficult to determine the original. One finds sometimes Laur, Laure, L'or, Lor, Lord, Lore, and Lort.
The present form "Lord" was probably adopted by deported and exiled families that voluntarily modified it to that form in order to please English authorities and to avoid a repeat of the past deportation of the Acadians. The illiteracy of the population of old Quebec and of the English administrators were no doubt also factors.