No. Bruce Lee had one son named Brandon Lee who died at the age of 28 filming The Crow. Correct spelling is Jet Li, but that is just a stage name. Jet Li's real name is Li Lianjie
Jet Lee has no relation to Bruce Lee. The last name Lee in China is a very common name. Just like the last name Smith would be a very common name in the United States.
When Long Feng hypnotized Jet to kill Aang, Aang reminded him of his despairing past, so Jet turned against Long Feng, but because of Long Feng's evil personality, he killed Jet and left the scene...