James embraced Williamson after the game before praising him during his locker room interview with reporters.
"It's my obligation and it's my job to continue to pass on the game to the guys that's coming in after me," James said. "That's just my responsibility. No one told me to do that.
"I just feel like it's my responsibility to leave the game in a better place than when I had it."
The Pelicans had a 33-29 lead at the end of the first quarter. Williamson poured in 11 points in the second quarter, but the Lakers had a 63-61 lead at halftime. James had 19 points in the first half.
The game stayed tight in the third quarter, with the Pelicans earning a 95-93 advantage entering the final frame. The Lakers responded with an 11-0 run in the fourth quarter to take a 106-101 lead with 7:24 remaining. New Orleans tied the game once down the stretch, but could not overcome the deficit.
James had 13 points in the fourth quarter. Williamson had 12 points in the final frame. The Lakers outscored the Pelicans 29-19 in the final 12 minutes.
"He is who he is," Williamson said of James. "He's an incredible player. I give respect when it's due. He hit a big shot that helped them seal the game."
Pelicans guard Lonzo Ball had 19 points, nine rebounds and nine assists in the loss. Derrick Favors had 12 points and 14 rebounds for the Pelicans. Kyle Kuzma had 20 points for the Lakers. Kentavious Caldwell-Pope scored 13 points off the bench for Los Angeles.
The Lakers (46-13) host the Philadelphia 76ers at 10 p.m. EST Tuesday at Staples Center in Los Angeles. The Pelicans (26-34) host the Minnesota Timberwolves at 8 p.m. EST Tuesday at the Smoothie King Center.