Physically Lebron would be fine, but mentally I don't think he would fair as well.
And it's the mental aspect that separates the greats.
LeBron has grown in the AAU era where everyone at his talent level is coddled and catered too. Everyone is friends, etc.
I feel the competitive nature of players is much weaker today then in the 80s and 90s.
Would he be mentally tough enough to deal with the physical play every night where he doesn't get calls and his competitors generally have a dislike for him?
Players respected each other back then but they didn't like each other all that much. They weren't friends and constantly hugging and going to dinner and stuff after games.
I do think Rodman would own Bosh. I think Pippen would destroy this shadow version of Wade and I think Jordan would obsess over finding the weaknesses in James game so much that it would be on his mind every waking moment. He would dream of it. I think he would find some and he would exploit them.
I think Jordan would own James from a mental standpoint.
I think James would be an All-Star in that era, but he doesn't have the mental toughness consistently, from what I have seen, to dominate that era to the tune of 4 out of 5 MVPs like today.