Prior to the events of the first Tekken game, Lee was shipped off to the U.S. to train with Marshall Law and Paul Phoenix by Heihachi (Lee's db+1+2 unblockable is the same as Paul's, he also shared the 'Shredder' kicks with Paul in TTT and T5 but could only do them out of Mist Step. Good juggle ender though). This is from his
Tekkenpedia entry. This is presumably why he does not use any Mishima Fighting Style Karate, even though Heihachi supposedly adopted him to groom him to become a rival to Kazuya. Stranger yet, he's had no side-stories to do with Law and Paul. All his story modes to date have revolved around his rivalry with Kazuya. Maybe he wasn't in the U.S. for that long? (he does speak Japanese in the games, not English, even though he resides in the Bahamas and is of Chinese origin. What a confusing man.)