Funny, I’m on the eastern side of the upper Midwest, grew up suburban/rural. The phrasing reminds me of using “learn” in place of “teach”, which I’m familiar with the concept of but haven’t heard used unironically.

Edit: I’ve been saying sentences with “borrow me [thing]” out loud and it’s possible that I just haven’t registered folks using it, rather than having never heard it. It sounds off but not alien.

fwiw I’ve never heard someone say that they can borrow someone something before. Might be a regional thing.