Lion's Tooth is the sword of Prince Joffrey Baratheon.
A Game of Thrones
While out riding with Sansa Stark, Prince Joffrey Baratheon comes across Arya Stark and a common boy, Mycah, playing at swords with wooden sticks. He threatens Mycah and cuts his cheek, which leads Arya to attack the prince with her stick. Joffrey then threatens Arya with his sword, slashing at her, until Nymeria bites him to protect her. Arya throws Lion's Tooth into the Trident.
A Clash of Kings
Now king, Joffrey receives a replacement sword, Hearteater. Sansa recalls how Arya had thrown Lion's Tooth in the river, and she hopes that Stannis Baratheon will do the same with Joffrey's new sword.
A Storm of Swords
Have no fear, lady. I am almost a man grown, and I don't fight with wood like your brothers. All I need is this. I call it Lion's Tooth.