"First of all, I want to continue to shed light on justice for Breonna Taylor and to her family and everything that's going on with that situation," James told the media after a scrimmage against the Dallas Mavericks.

"We want the cops arrested who committed that crime."

James -- along with the rest of the NBA -- is pushing for social justice during the league's return to play ... especially for Taylor, who was killed by 3 Louisville police officers in her home in March.

"As one of the leaders of this league, I want her family to know, and I want the state of Kentucky to know that we feel for her and we want justice. That’s what it’s all about. What’s right is right and what’s wrong is wrong."

As we previously reported, Taylor's family is well aware of the advocacy led by the NBA superstars ... and Breonna's mother told TMZ Sports she is grateful for their actions.

"Everyone raising their voices for justice are what keeps this family going each day," Tamika Palmer told us.

LeBron -- who etched ""#Justice4BreonnaT"" on his sneaker for Thursday night's scrimmage -- also weighed in on Black Lives Matter ... clarifying it's not a movement, but a lifestyle.

"When you're Black, it's not a movement," James said. "It's a lifestyle. We sit here and say it's a movement, and, okay ... how long is this movement going to last?"

"'Don't stop the movement.' ... No, this is a walk of life. When you wake up and you're Black, that is what it is."