My only quibble with your "there is literally no permutation of events, no alternate universe" take is injury and other bad luck. I suspect for every Lebron -- who's been lucky enough not to be in the wrong place at the wrong time, injury-wise, for decades -- there are a number of equal/better players (physically and mentally) who get bumped, land wrong, tear an ACL, and their trajectory changes forever. (Or get in a car accident, or... etc, etc.)
The underappreciated part of luck (by the lucky) is not the good luck people have the benefit of, it's the bad luck they avoid.
See this just isn't true. Durability is a physical property and in this area, like many others, LeBron is just on a totally different level than pretty much everyone else. The number of minutes he has played + the low amount of offseason he has (consistent deep playoff runs) + the physicality of his game + the few injuries he has sustained strongly suggests that he has a rare durability.
I really think you are underestimating how special LeBron is, how obvious it has been since he was in middle school, and how much it says about his physical gifts that he has played such heavy minutes for so long. We still talk about high school prospects being the next LeBron James because he was obviously a once in a generation talent (Zion being the only prospect since LeBron that has equalled his hype). Also LeBron has not really had good luck in his life. He had talent that transcended his terrible situation.
Certainly an ACL tear or other catastrophic event would have altered his trajectory.
On a human level, it is worth appreciating such things. Finding new ways to express and experience gratitude is one of the most profoundly powerful things a person can do. A true key to happiness. (I hope this doesn't sound sarcastic: I really believe this)
I think we just generally leave that sort of thing out of "what makes Lebron, Lebron?" type discussions because it's a constant for all athletes. A catastrophic injury would disrupt any player's trajectory. That's not interesting or useful to discuss from an analytic standpoint.
What we're really looking for is, "why is Lebron different from others who've avoided catastrophic events?" or to be more on-topic, "why was Levandowski able to rise to superstardom when other engineers weren't?"
Certainly, yes, some of this can be chalked up to Levandowski's avoidance of catastrophic events. He wasn't eaten by bears! His parents didn't blind him with acid! He wasn't struck by meteors! But, this is also true for a lot of other engineers, so this doesn't tell us anything useful. Everybody already knows that being killed by a bear is detrimental to one's career prospects.
To return to (and hyper-focus on) Lebron for a second...
there are a number of equal/better players (physically and mentally)
who get bumped, land wrong, tear an ACL, and their trajectory changes forever
In his case, the numbers suggest that the number of "better-than-Lebron players who don't make it" is extremely small and likely zero.
1. Every year, millions of people play basketball and do not suffer catastrophic incidents and yet also do not display the sort of generational talents displayed by Lebron.
2. Given the extremely large sums of fame and money involved in collegiate/professional basketball, anybody manifesting his level of talent is unlikely to go undiscovered. There is a lot of incentive for everybody involved to identify and develop such talent. This would be less true for many other pursuits. I suspect there are many "undiscovered Bobby Fischers and Gary Kasparovs" out there in the chess world and many "undiscovered Lewis Hamiltons" in the racing world; I suspect this is not the case for "undiscovered Lebrons."
3. Basketball is also different from other pursuits in that freakish physical height is a great advantage. If you are tall, in most of the world, people will tell you to play basketball. A height of 6'8.5" (Lebron's height) is something like 99.99th percentile and playing basketball is one of the few lucrative things one can do with that height, unlike a 99.99th percentile intelligence or even 99.99th percentile strength.
The underappreciated part of luck (by the lucky) is not the good luck people have the benefit of, it's the bad luck they avoid.