A 'Rocky' movie where Balboa goes up against a true martial arts champion?
Lee gets a contract with Warner Brothers for additional films, probably co-starring Chuck Norris, Kareem Abdul-Jabbar, his son Brandon, and possibly even Jackie Chan at the beginning of Chan's career. (and I'm not being completely facetious up above--Stallone and Schwarzenegger could also appear in Bruce Lee movies at least until they become headliners themselves).
If Jackie Chan's career can be seen as a model, Bruce Lee will probably transition to more dramatic roles as he gets older, downplaying (but not completely eliminating) the martial arts aspects of the parts. Lee's ambition was to be taken seriously as a dramatic actor and he did have the talent. Lee's accent is what hindered his acceptance by American studios, but as he gets older and more experienced with using English his accent will moderate with time--not unlike what has happened with Arnold Schwarzenegger, who had to be dubbed for his first few movies. Eventually Bruce Lee will become a director and producer, perhaps in the Hong Kong film industry.
Jeet Kune Do, Lee's personal martial arts style, is seen in OTL as a precursor to modern Mixed Martial Arts. I can see Lee becoming deeply involved in MMA as well, if not as a fighter then certainly as a manager/promoter.
I can also see Lee becoming a political activist, particularly over matters such as the Tienanmen massacre and the sovereignty of Hong Kong.