James, a four-time NBA most valuable player, signed with the Lakers in July after leading the Cleveland Cavaliers to four straight NBA Final appearances, including their first championship in 2016.
He has played in every NBA Finals since 2010, also winning titles in 2012 and 2013 with the Miami Heat.
James had 26 points, 12 rebounds and six assists in his Los Angeles debut against the Trail Blazers in Portland on Thursday night, but the Lakers lost 128-119.
The Lakers will likely need a better start with their long-range shooting against the Rockets. Los Angeles missed its first 15 tries from 3-point range before finishing 7 for 30 (23.3 percent) against Portland.
James said he and his new teammates are still going through a feeling-out period.
"It takes a while to get to where you can close your eyes and know exactly where your guys are," he told reporters after his Lakers debut. "It's going to take patience from our team, from all of us, to just figure out one another, figure out what we are good at, figure out what we are not so good at, how we can be better at it."
The Rockets returned their core players from last season's team that lost to the Golden State Warriors in the Western Conference Finals, and they added 10-time NBA All-Star forward Carmelo Anthony to the mix. They seemed to run low on energy in their season opener against the visiting New Orleans Pelicans on Wednesday night, however.
After getting outscored by 17 points in the first half, the Rockets were unable to generate a push against the Pelicans and lost 131-112. New Orleans shot 53.1 percent from the floor.
"I thought they were tired," said Rockets coach Mike D'Antoni, who coached the Lakers for two seasons (2012-13 and 2013-14).
James Harden, who averaged an NBA-leading 30.4 points last season en route to winning NBA MVP honors, was held to 18 points on 6-for-15 shooting.
Anthony, who played the last season with the Oklahoma City Thunder, scored nine points off the bench on 3-for-10 shooting.
Harden, a Los Angeles-area native, is averaging 30.3 points in 32 career games against the Lakers.
One of the bright spots for the Lakers in their season opener was the play of reserve shooting guard Josh Hart. The second-year player scored 20 points on 8-for-12 shooting, including 3 for 5 from 3-point range.
Hart played 27 minutes, the same as starting shooting guard Kentavious Caldwell-Pope. who was limited to five points on 1-for-3 shooting from the floor.
Hart didn't want to talk about his offense afterward, but rather how he could improve on his defense after Portland reserve shooting guard Nik Stauskas scored 24 points and shot 5 of 8 on 3-pointers.
"Just got to make sure we get the adjustments down and get better on defense," he told Spectrum SportsNet.