Despite the defeat, the Hornets finished the day half a game ahead of Atlanta in fifth place in the East, after the Hawks fell 126-102 to the Denver Nuggets.
The Cavaliers also built an early six-point lead, but the Lakers surged ahead later in the first quarter behind James, who scored 17 points in the period on 6-of-7 shooting from the floor, including 4-of-5 success from 3-point range.
James and Davis scored 26 points apiece as the reigning NBA champions escaped with a victory that kept them unbeaten in four road games this season and improved their record to 6-2 overall.