With this line, you are placing the key inside the location again. The idea was to start out with the key completely out of play. And you don’t need the “revealed” lines.
Try this:
The Lab is a room.
The dirty door is a door. It is locked. It is east of the Lab and west of the Annex.
The statue is in the lab.
Locke's Hand is part of the statue.
Locke's Hand is a container.
Locke's Key is a thing.
Locke's Key unlocks the dirty door.
Before examining Locke's Hand for the first time:
now Locke's Key is inside Locke's Hand;