I was typing up my response on why I thought he wouldn't do it, but then I did the math and it seemed pretty attainable.
LeBron needs 13,474 more points to catch Kareem. If he plays 10 more seasons, and does the following, he'll be just about there (the following gets him 13,424):
Age 31, Games Played 72, PPG 23
Age 32, Games Played 72, PPG 23
Age 33, Games Played 72, PPG 23
Age 34, Games Played 72, PPG 23
Age 35, Games Played 68, PPG 20
Age 36, Games Played 68, PPG 20
Age 37, Games Played 68, PPG 18
Age 38, Games Played 68, PPG 16
Age 39, Games Played 68, PPG 14
Age 40, Games Played 68, PPG 12
I think it's a pretty safe assumption to say LeBron's never playing 82 games again (actually he's never played 82 games in the first place). Even if 100% healthy, he's taking some games off every season.
We'll see consistent strong scoring over the next 4 seasons, but maybe with some decline as he tries to facilitate more and lets Love and Irving (or whoever) take more of the scoring load.
Age 35-36 will probably be that drop off, when he's still an All-Star, but not automatically All-NBA. And as he gets older he'll need more rest and probably incur a few more at least minor injuries, so we're dropping a few points and games from his averages.
Then if he sticks around, age 37 is when we'll see a more noticeable decline in production each year.
I like to think those assumptions are reasonable, though some may disagree.
I appreciate the effort you put into this, but again, this really seems to undersell the decline. You look at guys that are complete shells of themselves right now, especially someone like KG. KG was "only" 38 this past season but was only capable of playing in 47 games and averaging 7 points a game. The season before that at 37, he only made it into 54 and was averaging 6.5. His last season with Boston at 36 was the last time he sniffed 15 points averaging 14.8 and even that was 68. What is the argument for saying Lebron will keep trucking along for so much longer than KG could and never hit a wall like KG could. If anything, Lebron will have played a ton more minutes because of playoffs and long playoff runs and has a heavier frame that puts more grind on his body.
Obviously it's harder to predict the further you go out, but I'm also underselling the present. LeBron's never averaged under 25ppg, but I have him doing that the next 4 years.
I think it's wrong to compare LeBron to KG, because KG has never been a scorer. Karl Malone and Michael Jordan both averaged 20+ppg until age 39. Kareem did it until age 38. Dirk just averaged 21 at age 36.
When most people are talking about LeBron's future, they're talking about a guy who will go down as probably the greatest player of all time, at least top 5. So it's very appropriate to compare him with the other upper echelon of all time greats, and while I love KG he ain't one of them.
So few have done it, but that's what makes this a possibility for LeBron. When his career is over, he'll likely have done a whole bunch of things that nobody or only a very select few have ever done.
he averaged 25 this year. As the teams talks about the need for him to cut his minutes to last through the whole season, this is not going to increase. So you are not underselling it at all.
I personally also think KG is a much better comparison than MJ. MJ retired twice and had 3 years of long playoff runs removed from his legs.
Any single high school to NBA player that was good seems to have flamed out a little earlier on in their career, and it only makes sense. Jermaine O'neal, KG, McGrady, Rashard Lewis, Kobe etc.
I don't get how we just ignore the fact that Lebron has already played the equivalent in minutes in his career of a guy that is 35 years old. Also just look at your example of Dirk, he is a perfect example of what I am talking about. Next year he will be 37. How many minutes will he play? How many will he average? He was at 17 this year and saw his minutes cut down to 29. What is fair for next year, 14, 15? He also is a player that does not rely on athleticism or strength at all, which is the opposite of Lebron.