Where do you find the lift key in Pokemon FireRed?

You find it on B4F in FireRed when you battle a Team Rocket Grunt in the far north corner he has a Level 21 Zubat and Koffing, if you defeat him, then he will drop the key. This will enable you to battle Giovanni. In Silph Co., you don't need a lift key to get anywhere, instead, you have to use the teleporters to get to the Card Key.