Trap Carl places directly in front of the sealed Prism throne room door as he abandons the castle.
As part of the loot-break-and-trap withdrawal from the Prism castle, Carl closes the throne room door on Lockjaw and sets a freeze trap immediately in front of it. It is one piece of the rapid trap lattice he seeds through the small castle while Princess Donut directs the looting — the throne room itself cannot be trapped, so the doorway gets the treatment instead.
The placement doubles as insurance on Carl's plan: anyone coming to usurp Lockjaw from the throne, likely Epitome Tagg's people, has to eat a freeze trap on the way in.
Door-guarding trap protecting Carl's throne-room gambit after the team withdraws.