Damocles is a figure in Greek Mythology. He was an excessively flattering courtier in the court of Dionysius I of Syracuse, a 4th Century BC tyrant of Syracuse, Italy. He exclaimed that, as a great man of power and authority, Dionysius was truly fortunate. Dionysius offered to switch places with him for a day, so he could taste first hand that fortune. In the evening a banquet was held, where Damocles very much enjoyed being waited upon like a king. Only at the end of the meal did he look up and notice a sharpened sword hanging by a single piece of horsehair directly above his head. Immediately, he lost all taste for the fine foods and beautiful boys and asked leave of the tyrant, saying he no longer wanted to be so fortunate.
In Tomb Raider, in St Francis' Folly Lara will explore a room dedicated to him. The room is lined with swords hanging from the ceiling. They will start to come down, when she's picked up the Damocles Key.
The level Greece - St. Francis Folly in Tomb Raider Anniversary also features a room dedicated to Damocles with falling swords in the ceiling. In addition there are smaller, retracting swords on the floor to make the exit from the room more difficult after retrieving the Key of Damocles.