LeBron James surprised the basketball team at Notre Dame High School in L.A. on Tuesday -- hitting the gym for a training session while his wife checked out the campus ... TMZ Sports has learned. 

We're told Bron and Savannah James rolled up to the school in a chauffeured car around 6 PM and walked around campus before a workout on the court. 

LeBron owns a home in Brentwood and there's talk he could be checking out various private schools to send his kids -- including 12-year-old Bronny, one of the best hoop prospects in the country. 

Notre Dame is one of the top private schools in the area -- with an alumni list that includes Giancarlo Stanton, Rachel Bilson, Dave Navarro, Katharine McPhee and Jerry Mathers

Any school would kill for Bron's kids -- but it's unclear if ND is seriously in the running. 

It's a Catholic school ... so ... pray?

10:55 PM PT --  LeBron has posted a video thanking the school for opening the gym so he could work out after a long day of shooting commercials.

LeBron insists the kids had no idea he was coming and emphasizes that he was there to get his own workout in.

LBJ makes no mention of the school being a candidate for his own kids. Sorry, Knights.

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