Do I need to mud drywall before applying ship lap?
I would say best practice would be to at least seal the drywall with a primer so it does not absorb the moisture in the humid post shower air. 

Code (may?) require the joints have at least a tape applied with a skim coat of mud for fire code. That is speculation on my part.

If the gaps in the ship lap will reveal the drywall you will want it a color of your choice.

Personally i would prime and paint it with a semigloss.