James was injured during the Lakers' 127-101 victory over two-time defending National Basketball Association champion Golden State on Christmas when he slipped while going for a loose ball.
James walked gingerly off the court in and video showed him wincing near the bench and telling trainers "I felt a pop" regarding the injury.
Since Rondo will now be out at least one month after having surgery, and it's unclear when James will return from his groin strain, it will be up to Ingram, Kuzma and Ball to keep the Lakers in games and be leaders.
"I take a lot of pride in (staying healthy)", James said after the Warriors game.
"We are obviously not going to rush him back", Walton said.
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Team doctors officially diagnosed James with the injured groin after an MRI exam on Wednesday.
James, who left the Lakers' victory over Golden State on Tuesday with the groin injury, had played 116 consecutive regular-season games; that number jumps to 156 when postseason games are included. "That could be an injury where if you come back too early you re-injure it and then you're out longer".
Lakers head coach Luke Walton said the decision on when James plays next will be made in conjunction with the superstar and the team's medical staff. "We've got to do a better job closing out games and just being composed". He has appeared in all 34 games this season and did not miss a game last season with the Cleveland Cavaliers.
James is averaging 27.3 points, 8.3 rebounds and 7.1 assists this season, his 16th in the National Basketball Association and first with the Lakers.