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 
That's what I thought.  The MEL is for safe  operation of the aircraft and passenger safety, not passenger comfort.  The Operations Manual would probably cover that.  I never had to deal with this specific issue, though.  The only lavatory issue I ever had to deal with was "if the lavatory blue water vent is leaking and the hydrolic tail bumper is inop extended, add 10% to fuel burn".  

  (MELs [Minimum Equipment List] are not written like I wrote it.  It's an "IF" + "AND" = "THEN" balance sheet format.)