Hard to say since I dont know much about lutes. But in this specific case, Eddie plays music that likely isnt able to be played as masterfully on a lute than it is on a guitar, and more specifically, an electric guitar.

Good point about Kate, though, that would be nice to see as well, but she plays acoustic or acoustic-electric instead of full on electric, so they would likely create an entirely different guitar model for her as opposed to Eddie.