You may call me
"The survivor who enters the lab will acquire the cure"
I'm pretty sure this refers to the cure token that will save the world from the zombie epidemic and not the antidote cabinet.
As soon as the lab door is open and you enter, the Nemesis appears. The multi-team tracker flips and you start the Final Showdown. Follow the instructions on page 29 of the revised rule book which start with:
"Players should note the following occurs once the survivor enters the laboratory: 1. The survivor who entered the laboratory takes the cure token."
Then to use the antidote cabinet, you spend 2AP just like any of the other corner room functions except the Sprinkler which is deactivated during the Final Showdown.
As to why it only shows up at the end? Well, thematically it makes sense since if you already had an antidote for the zombie epidemic you wouldn't need to go into the lab. Also, during the Final Showdown, once you die you don't respawn another survivor. You die, you are eliminated from the game. The antidote cabinet is one last chance to keep from turning into a zombie.