The 36-year-old, playing on the eve of the first anniversary of Bryant’s death, finished on 46 points.
It was his second-highest total as a Laker and the most against his first NBA team.
He added eight rebounds, six assists, two steals and two blocks.
James, playing for the second time in Cleveland since he switched to the Lakers in 2018, scored 13 points in the final four minutes and 41 seconds.
It helped the Lakers pull away and claim a 10th win out of 10 on the road this season.
They play in Philadelphia, Bryant’s birthplace, on Wednesday in what will be an emotional occasion.
Anthony Davis had 17 points and 10 rebounds for the Lakers, while Montrezl Harrell scored 15 off the bench.
For the Cavaliers, Andre Drummond had 25 points and 17 rebounds while Cedi Osman scored 20 points and Collin Sexton finished with 17.
The Orlando Magic won for only the second time in their last 10 games, beating the Charlotte Hornets 117-108 in the first regular-season NBA contest in history with two female officials.
Natalie Sago and Jenna Schroeder, who are among the seven females who have officiated in the NBA this season, worked with Sean Wright in the game in Florida.
“This is a big deal,” Schroeder told the NBA website. “It’s like my feminist dreams come true, that like my personal values are colliding with my professional values and it’s awesome.”
“It’s amazing,” Sago added. “I’m just proud to be part of an organisation that promotes people to do the job based on our abilities, not on our gender, race, ethnicity, those types of things.”
Elsewhere, Malcolm Brogdon scored 19 of his 36 points in the second half as the Indiana Pacers beat the Toronto Raptors 129-114.
Indiana All-Star Domantas Sabonis injured his left knee in the first quarter and will have a scan on Tuesday.
Stephen Curry scored a game-high 36 points as the Golden State Warriors thrashed the Minnesota Timberwolves 130-108, overshadowing Andrew Wiggins’ reunion with his former side.
The Detroit Pistons ended a four-game losing streak in a 119-104 win over the Philadelphia 76ers while the Oklahoma City Thunder defeated the Portland Trail Blazers 125-122.
The Brooklyn Nets pulled away in the final minutes for a 98-85 victory over the Miami Heat while Michael Porter Jr. scored 30 points and Nikola Jokic added 20 points and 10 rebounds as the Denver Nuggets beat the Dallas Mavericks 117-113.
Jaylen Brown scored 26 points and Jayson Tatum added 24 in his return from NBA coronavirus protocols as the Boston Celtics started a run of seven out of eight games on the road with a 119-103 victory at the Chicago Bulls.