Lu Ten was the beloved and only son of Iroh, cousin to Zuko and Azula, and grandson to Fire Lord Azulon. Little is known about him right now, but he seems like he was a happy boy and close with his father. He was also in line for the Royal throne since Iroh was to be the next Fire Lord.
When Lu Ten was older, he was involved in the battle waged against the Earth Kingdom capital Ba Sing Se -probably as a soldier-, which (General) Iroh was leading. But something happened, and Lu Ten was killed. Iroh was devastated, and soon after abandoned the siege of Ba Sing Se.
A grave on a hillside with a stone lantern and pond was made to honor Lu Ten; assumably located in the Fire Nation. On one occasion, an older Iroh visits and vows "I will see you again."
On a related note, there is a theory that one of Koh the Face Stealer's faces is that of Lu Ten. There's no real proof of this, but the face is similar to Iroh, Iroh has been to the Spirit World, and special emphasis was given to that face. But like I said, it's just a theory. However, I do feel that some questions regarding Lu Ten will be answered in the near future.