Okay, just for discussion's sake, let's pretend we still have Cousins and we do that trade.
Picture this: Lebron signs his contract with the Kings, walks out of wherever the signing takes place, and strolls nonchalantly towards his waiting vehicle. In doing so, his path takes him along a sidewalk where above him a wonderfully fabulous banner announcing his arrival in our fair city waves in the morning breeze. As he walks by, waving to the horde of cheering fans, a strong gust of wind comes up. It catches the banner, which whips away from the workers, and blows in LBJ's direction. It startles him, and he steps aside to avoid being hit - right into the path of an oncoming truck.
That, my friend, is why we don't trade for LBJ. It would inevitably mean his doom. That's just how luck rolls for the Sacramento Kings.