The occupation is lath render, not lath renderer.
To render means to offer. To rend means to split. Both words have largely fallen out of use, but they linger on in phrases like "Render unto Caesar that which is Caesar's" and "What God has joined together let no man rend assunder."
A plasterer certainly renders plaster, but a lath render certainly doesn't render wood, he rends it - he splits it into laths. The laths would be used for trellis work or to make plaster & lath walls, and I suspect that this partly explains the confusion between render & rend. To call a lath render a renderer is like calling a plasterer a plastererer. It's a common mistake today, but I think you'll find the Victorian census enumerators usually got it right.
As if to prove my point, the spell-checker on this site has just (correctly) challenged renderer as well as plastererer.
