In order to find the proper exit, follow the running rats. You should take the following turns: left, left, right. On your way you should also light up the cressets that you pass by. That way it will be easier to return in case you make a mistake.
At the end you will find a locked door which you have to picklock. Do it just like you did it in previous sequences: start off by turning the left and right analog sticks until the lock clicks. Afterwards, while still holding both sticks, start pressing the free run button. The mission will end after you open the door.