LeBron James is looking forward to talking about his thrilling matchups against Stephen Curry with his grandchildren.

That is how much James relishes going up against the Golden State Warriors star, as the duo served up another wonderful instalment of their long-running rivalry on Saturday.

James and the Los Angeles Lakers came out on top, edging out the Warriors 145-144 in double overtime.

Curry led the game with 46 points, with 15 of those coming across the two OT periods, but James inspired the Lakers with a triple-double of 36 points, 12 assists and a career-best 20 rebounds.

"It's something I'll be able to talk about with my grandkids," James said.

"When you talk about me being able to compete versus one of the greatest players to ever play the game.

"It's been a treat to go against one of the greatest to ever play this game.

"For us to continue to push each other at the state of our careers, you don't take it for granted because you don't know how many times you're actually going to get the moment to actually be on the same floor with such a talent."

James and Curry dominated four successive NBA Finals, and the pair, who have eight championship rings between them, rekindled that fire in magnificent fashion.

However, neither team have been enjoying their best campaigns. The Lakers are ninth in the Western Conference with a 24-23 record, three places ahead of the 19-24 Warriors.

"Every year that we get to do this and go back and forth, the battles, the Finals runs, the playoff battles last year, after the horn sounded tonight there was a little laugh of, I can't imagine a scenario where a game like tonight happens, [with] him in Season 21 and me in Year 15," Curry said.

"You look forward to the battles, but you also appreciate the mutual respect of what it takes to keep doing what you're doing at this level. Only a few people know how hard it is. I'm happy to be in that group."

Klay Thompson, who scored 24 points for the Warriors, is simply happy to have played alongside, and against, two of the NBA's greatest.

"Credit to LeBron for what he's doing at his age. I mean, that guy is a freak of nature in terms of his ability to play at this level for so long. Same with Steph," Thompson said.

"When you're younger, you don't ever really think that basketball will stop because it's what you love. It's all you do.

"But when you get to your thirties, you realise there's an end point to being an athlete. Knowing that, I am very grateful to step on the floor with those guys and play against LeBron."