During the episode "maroned", Lister cuts a guitar shaped bit of wood from Rimmer's Camphor wood chest using his Les Paul copy as a template. The cut out looks ok but right at the end, where you see the actual hole, notice how the hole is shaped NOTHING like a Les Paul!!!
Another thing you've gotta notice is that the shape and size and design and the guitar in general change heaps of times through the series. The guitar that the Cat breaks in Emohawk: Polymorph II is a completely different shape to the one that Lister plays in The End
1) The guitar is a Les Paul copy, therefore will not look like a Les Paul.
2) Lister may not know what a
Lles Paul looks like, and may have been told that it's a Les Paul copy.
3) His guitar changes from acoustic to electric because Lister puts the acoustic one in storage and get's the electric one out of storage.