Lion's Tooth was the gilded sword Prince Joffrey wore on the kingsroad as the royal party rode south to Winterfell and back. Like Hearteater after it, it was a costly toy of ordinary steel, named for the Lannister lion of his mother's house.
Joffrey lost it on the journey. When he drew it on the butcher's boy Mycah and on Arya Stark beside the Trident, Arya beat at him with a stick and her direwolf Nymeria bit his sword arm; Arya snatched up the fallen blade and flung Lion's Tooth into the river. It was never recovered.
Status: lost in the Trident.