If a lavatory is inoperative, that aircraft is going to be restricted to flight legs that are relatively short because everyone realizes how uncomfortable it can become when you're not able to go. I haven't looked up the specifics, but the limitation would be outlined in the minimum equipment list (MEL).

MEL is a list where everything on the aircraft that can be broken is listed and what must be done to operate the airplane safely.

On the airplanes I fly, the lavatory is of a recirculating type, where the blue fluid is filtered and re-used, but at some point the waste holding tank would become full. Which is probably a smaller problem on international sized aircraft, but on the smaller 50-100 seaters, for example, the system wasn't designed to be utilized all day without servicing.