According to lore, the Iron Throne was made up of all the swords that were surrendered to Aeryn Targaryen. According to the above picture, Gandalf was among the conquered. You can see what appears to be his sword tucked behind Joffrey’s head. There’s really no explanation for this, but we haven’t seen Peter Jackson’s third Hobbit film. Who knows what he’s got up his sleeve?
Then again, the prop makers behind the throne probably used whatever they could get their hands on—which means other famous swords might be lurking in the chair. Happy hunting.