SC6's Michael Smith explains why he wants LaVar Ball to quit taking shots at NBA players, with the latest star being LeBron James. (0:43)

A day after LeBron James told him to "keep my kids' name out of your mouth," LaVar Ball doubled down on his opinion that the children of star athletes don't themselves become star athletes.

"I gave an opinion on what I felt about no superstars' kids really being superstars and the fact that they have to live up to their parents or to their fathers or whatever. I have yet to see one, and I've been around for 50 years," Ball said in an interview with SiriusXM's "Full Ride" on Wednesday. "Have you seen one where the superstar's son is just as good or better than him? I said a superstar. I ain't saying just a regular player. I'm talking about a guy who we picture as an icon -- a Dr. J, an Allen Iverson, a LeBron James. If somebody asks me a question, I'm gonna give them an answer."

Ball had made reference to James' sons, LeBron Jr. (12 years old) and Bryce (9), which prompted the elder James' response.

"He can talk all about his brand, talk about his sons, talk about basketball, talk about me," James told ESPN on Tuesday. "But keep my family out of this."

Not content to just reiterate his point, Ball also went on the offensive against James on Wednesday.

"I don't care what LeBron said," Ball said. "He talking about he warned me. He warned me for what? What is a warning going to do? Nothing."

Ball also referred to James as "touchy" a day after the four-time NBA MVP told ESPN that Ball's invocation of James' family is "a problem now."

Despite having a problem with LaVar Ball, James said he has nothing but respect for Lonzo Ball, a standout freshman for UCLA, who is the eldest of LaVar's three basketball star sons.

"I actually like [Lonzo]," James told ESPN on Tuesday. "I like his game."