Reigning NBA champions the Lakers, without the injured Anthony Davis, won 117-115 with James adding seven rebounds and seven assists.
Zach LaVine top-scored for the Bulls with 38 points, 19 of which came in the first quarter.
Elsewhere, Stephen Curry scored 38 points as the Golden State Warriors beat the Los Angeles Clippers 115-105.
The Warriors netted 20 three-pointers to avenge their defeat by the Clippers on Wednesday, bouncing back from 22 points behind to secure their fifth win in seven games.
"I think our guys just hung in there," said Warriors head coach Steve Kerr.
"They kept their energy up. They kept their spirit up. They were pumping each other up on the sidelines. It just felt like we were on the ropes, but we hung in and that's what matters."
The Boston Celtics won their sixth game in seven as they saw off the Washington Wizards 116-107.