Lebron didn't shoot well but he made great passes, forced the defense to key on him, set picks to get his teammates open, and did all the little things right.
Lebron made the right plays. The Spurs were zoning Lebron and doing soft doubles every time he got the ball. They constantly shifted to his side to cut off the lanes for drives and double when he tried to post up. So he shot passes and pushed the ball to teammates who were open. Why do you think Bosh was constantly open in mid/range? Duncan was patrolling the paint to stop Lebron. It's why Wade and Chalmers were able to attack and get into the paint.
The Spurs are doing the Maverick defense which is force Lebron to shoot and make everyone else beat you. Lebron is just a smarter passer and player than he used to be plus hes willing to the dirty things like set screens and throw hockey assists.