James added 11 rebounds and 11 assists to record his third triple-double of the season in a 132-123 win in LA.
Russell Westbrook finished with a triple-double of 24 points, 12 rebounds and 10 assists, while Malik Monk scored 25 points and Carmelo Anthony 24.
Jalen Green responded with 24 points as the Rockets lost a fifth straight game.
James, who this month became the fifth player in NBA history to record 100 triple-doubles, started at centre for the first time in his career.
Stephen Curry became the first player to make 3,000 three-pointers in a career but the Golden State Warriors lost 89-86 to the Denver Nuggets.
Will Barton scored four of his 21 points for the Nuggets in the final 43.6 seconds, adding to Nikola Jokic's 22 points, while Curry scored 23 for the Warriors.
Joel Embiid scored 36 points as the Philadelphia 76ers won 114-109 at the Toronto Raptors, with Tobias Harris adding a 19-point triple-double, including a career-best 10 assists and 12 rebounds.
The Sacramento Kings beat the Oklahoma City Thunder 117-111, Tyrese Haliburton recording 24 points and 10 assists as the hosts earned only a third win in 10 games despite Shai Gilgeous-Alexander's 33 points for the Thunder.