The lavatory is not a required item for dispatch on most airplanes.

Here are the MMEL remarks for the 737 series airplanes.

Associated lavatory system(s) may be inoperative provided:
a) Associated components are deactivated or isolated to prevent leaks,
b) Pilot-in-Command will determine if flight duration is acceptable with a forward lavatory unusable, and
c) Associated lavatory door(s) is secured closed and placarded “INOPERATIVE – DO NOT ENTER”.

Assuming most airplanes would have similar remarks, I'd guess it is pretty much up to pilot discretion, so you should hope that your flight crew likes to drink a lot of coffee!!!

- Eric