Go back to the room, where Raven is (the door on the right of the fountain - on the left of the door, there's a steel cart loaded with stuff) and talk to him. Show him the key blueprint. He will suggest that Kate should send the key to be repaired. She can send it by a Jukol owl.
Go to the balcony (the window with greenish curtains on Raven's right) and click on the magnifying glass icon on the pillar in front of you. Try to draw the attention of the owl sitting on the top of the tower. When this doesn't work out, go back to Raven and tell him you failed - he'll tell you that bait is needed.
Leave the room and go left. Go past the Doctor's office and head through the open, sky-blue door. You will notice a man sleeping on the bench - zoom in and steal Anton's key. Now take the corridor left from the brown door and enter the room.
Proceed into the passageway and then left - you will arrive at an aviary with mechanical birds. Zoom on the locked door and use Anton's key on the lock. When you get inside, take the mechanical bird on the left.
Go back to Raven and head through the balcony. Click on the magnifying glass icon on the pillar in front of you and place the bird on the windowsill right from Kate. Wind the bird up to lure the owl.