This key is on the opposite side of the door to the main foyer and is more useful when you are making your escape once you are done with the lord regent.

To get the key go past the first light wall off the main foyer. Take a right and you will go down a short hallway to a door. This opens into a narrow service corridor. Watch out this is regularly patrolled bu guards and the odd maid. Take another right and go past the security room and down a staircase to the kitchens. Take aa left and the key is on the wall on the right side through a door and a super short corridore that ends with the door to the foyer.