LAV's are frequently MEL'd. If it is a full flight, cross country, or an international, we would generally attempt to fix it first depending on its routing, etc. The call to fix it or MEL it was made by maintenance control, not the mechanic at the gate. We would troubleshoot during the turn and if looked like we would not be able to get it back before boarding time, we would ask MC if they wanted us to continue and hold boarding, or to defer it per the MEL.
If we MEL'd the lav, routing would generally change it to make sure it went to a RON with maintenance that night.
As for the procedure, we would make sure the lav was dumped, pull the C/B (if applicable), placard the door with the large, stick on, "LAVATORY INOPERATIVE - DO NOT USE", placard,. Every station had those on hand. As for that tape job, well, if that was all they had and the flight needed to go, I think I could have made it look a little more professional than that.
The MEL placard tab would also go next to the door lock indicator and the large Mel placard went into the inside cover of the logbook.