Esquire magazine and Apparel Arts Quarterly answered this question in the '30s. They wrote that the Lords' Hat wasn't named for any individual lord, but for the House of Lords, some of whose aristocratic members favored this type of hat.
Okay, it still begs the question as to why the name crossed the Atlantic. It wasn't as if we didn't previously have a similar style. Perhaps it grew out of the closer relations between Great Britain and the United States in those years.