I think publishers in the young United States, having no copyright laws on sheet music, blatantly copied sheet music from British publishers. However, I'm not able to find a source on that.
Did he? There's no evidence for that.
To me, it sounds like a smart Harvard grad just figured out a few missing pieces required to get textile manufacturing going. Wasn't his first time doing industrial processes at scale either: he successfully ran a distillery before that.
It's also interesting to remember that it happened at a time England was in open war against the United States. It's not really the same right now with Chinese companies trying to get into the US market and vice versa. Both countries claim to be allied but there's a clear disregard for the laws of one particular country!
Maybe a better analogy to what Francis Lowell did would be operation paperclip. The US did steal technology from Germany at the end of the war [0].
Was it really stealing?
The British pretty much did nothing to stop it nor protected their IP. They certainly didn't strongly enforce it.
Contrast that with Chinese theft; as soon as counterfeit products or patent infringing ones make it to US soil they are promptly seized and destroyed if found to be infringing the laws.