He finished a guy off in Enter the Dragon with an arm bar.
Jiu-Jitsu is a Japanese battlefield art that was modified by the Gracie family when they brought it to Brazil. They dropped out a lot of tactics that you can't train easily, like eye gouges, and added tactics that work well only in a controlled fight with rules - like a triangle choke and other blood chokes.
My trainer has a background in the old school Japanese jiu-jitsu. The first contact is typically a strike to the eyes and throat while kicking to the crotch at the same time. As the guy goes down, they would grab a wrist or an arm and break it, then maybe follow him to the ground for a very brief moment to grind the broken bones together. All of this takes 3-5 seconds and the Samurai would leave that guy behind and go on to the next. That is how the Japanese Empire stood against attackers for a thousand years until guns and artillery came into use. Being brutal is really the most effective way to fight, although most people, myself included, have a hard time gouging out anyone else's eyes.
Not only do I think Bruce Lee would do well in mma, I think if we took away all the rules, he could easily take Brock Lesnar. But then Lesnar wouldn't have eyes or nuts left and would never fight again, so these are merely philosophical matters.