James eventually finished with 35 points but it was a bittersweet night as the Lakers lost 113-112.
The 38-year-old forward, who started his career with the Cleveland Cavaliers and also played for the Miami Heat, has averaged 29 points per game this season.
A four-times champion and four-times MVP, James is on course to break former Lakers center Abdul-Jabbar's 34-year-old record of 38,387 points in the coming weeks.
When James turned 38 last month, Abdul-Jabbar had wished him happy birthday with the message: "38 is the new 38,388."
James is now 363 points behind Abdul-Jabbar and based on his scoring average, NBA statisticians expect him to break the record before the All-Star break next month.
In January 2006, the 38-year-old became the youngest-ever NBA player to reach 5,000 career points.
He reached the 10,000-point milestone in 2008, at 23, and in 2013 he entered the 20,000-point club.
In January 2018, LeBron dropped more than 30,000 points, with only seven players in NBA history to date.
He has a career-scoring average of 27.2 points per game.
