B757-300 Flight Attendant reported a chaotic flight after being dispatched with only two working lavatories.

Narrative

During boarding maintenance closed and tagged mid lav (Lavatory) as INOP (Inoperative). Reason not known. After first economy cabin service passengers started lining up to use the aft lavs. There were at least two people or more in line. Passengers started coming to first class cabin to use lav. I asked passenger to wait in line behind curtain. There were at least as many passengers in this line. When a first class passenger got up to use the lav; the passengers in line would get upset because they felt the first class passengers should wait their turn. The lines to the lav continued throughout the flight. Passengers would not sit down when the seatbelt sign went on because they didn't want to lose their place in line. Passengers in their seats were upset with the passengers in line. Passengers crowding in the aft galley nearly toppled the beverage cart being set up for second service. Needless to say; no second service was possible. FAs (Flight Attendants) couldn't get in the aisle to do water service. It was a very unsafe situation for all passengers and crew. This aircraft holds too many passengers for [only] 2 working lavs.