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.