James missed Thursday's 107-104 loss to the Oklahoma City Thunder, and another source familiar with the injury told ESPN that the Lakers' medical staff "wants to take their time" with James' recovery.
"Anytime LeBron's out and he's going to miss some time there's obviously concern," Lakers coach Frank Vogel said before Thursday's game. "Hopefully this is something that's minimal, and hopefully he'll be back soon."
James, a 19-year veteran who turns 37 next month, has already missed two of the Lakers' first eight games through their 5-3 start to the season because of a sore right ankle.
In the fourth quarter of Tuesday's game, James started to feel the injury but was unaware of what caused it.
"When he came over to the bench he just said he felt something pulling, was able to finish the game, but then obviously discovered there was something there after the game," Vogel said.
Vogel said the injury is unrelated to the groin tear that caused James to miss 27 games during the 2018-19 season.
Vogel added that James' early-season injuries have not changed the team's approach to protecting him for the long haul.
"Not any different than in years past," Vogel said. "We want to be responsible with his minutes ... get to the finish line as healthy as possible but also as in rhythm as possible. And that's a balance that we strike throughout the year."
James is averaging 24.8 points on 46.7% shooting -- his lowest percentage since his rookie year -- along with 7 assists and 5.5 rebounds per game.
"Obviously you can't replace what LeBron does," Vogel said, "but everybody else has to do what they do better and you have to start that way."