Which version of the game are you playing? In Previously versions, while completing this quest, you could accidentally leave the second floor of the tavern before finding the room.
But in the new version, this should have been fixed.
You needed to click on all the doors on the second floor of the tavern: read 2 dialogues, watch the scene with Lillian, and then you would automatically start a dialogue that would take you to the Spy's room.
Try loading an earlier save, or, unfortunately, start a new game.