Let's nip this one in the bud right now: Despite what this short video appears to show and what Reddit says, LeBron James didn't get T'd up for apologizing to Gerald Green.
The technical was called for an elbow to Green's face, as Green attempted to intentionally foul James in the closing seconds of last night's 103-97 Miami win. The confusion comes for two reasons. First, the slow-motion makes it appear that referee Karl Lane only called the foul after James approached and began to speak to Green, when it reality the whistle had come on the elbow. Second, techs aren't assessed for live-ball physical contact, but Green had successfully fouled James, so the elbow came after the play was dead. (There are elbow-specific rules for assessing technical fouls in the rulebook, but since James wasn't ejected, we know they didn't apply here.)
It's still a horrible call. James barely raised his arm and made, at most, glancing contact with Green, while Green appeared to embellish it. But sadly, crappy officiating on its own isn't news anymore.