Anthony Davis scored 34 points for the Lakers, with James adding 25 points and nine assists.
Jimmy Butler had 23 points for the Heat, who lost point guard Goran Dragic and forward Bam Adebayo to injury.
James said: "The job is not done. We're not satisfied winning one game."
Speaking after Thursday's game, he added: "You have to get a feel for how hard Miami plays. We got a sense for that. We got more work to do. It's that simple."