The elder O'Neal went on to have his No. 34 jersey retired by L.A. in 2013 and was enshrined in the Naismith Memorial Basketball Hall of Fame in 2016.
Yet when the younger O'Neal reported to the Lakers practice facility for a pre-draft workout on Tuesday, it wasn't with his father's blessing.
"We kind of bump heads about this process," O'Neal, 22, said on a video news conference. "He wanted me to stay in school. I wanted to better myself through this. He knows I'm working out with teams. But I'm not going to lie, we ain't talked about this. I'm kind of just going through it. He didn't do any pre-draft workouts; he just got straight on the [Orlando Magic], so it's a different grind.
"So, he didn't want me to do this, and I know he probably doesn't want me saying this, but sorry. We're both grown, we'll get past it."
His averages of 2.6 points on 40.5% from the floor, 3.0 rebounds and 0.4 blocks pale in comparison with his father putting up 21.6 points on 61% shooting, 13.5 rebounds and 4.6 blocks per game for the LSU Tigers before going No. 1 to Orlando in the 1992 NBA draft.
The draft prospect pointed out that the production can't be judged in direct comparison after he underwent open-heart surgery as a freshman and later dealt with foot and ankle injuries that sabotaged his last two seasons at LSU.
"I feel like me and him have a whole different story now," O'Neal said when asked if he felt any pressure following his father's legacy. "I went through some things that he didn't go through. He was the No. 1 pick in the draft. I kind of had to grind to get here. I had to grind a lot. I had to go through some stuff these past four years -- foot injuries, heart surgeries -- and I don't really look to be in his shadow."
He credits Lakers athletic trainer Shane Besedick, who used to work with UCLA, for saving his life by discovering the right anomalous coronary artery issue in their time with the Bruins.
"I know it's always going to be there, the comparison," O'Neal continued. "Every kid is going to get compared to their dad who does the same thing as them. So that's going to be there. It doesn't bother me."
O'Neal -- a power forward at 6-foot-10, 215 pounds compared with his father who played center at 7-1 and north of 300 pounds -- said he was determined to stay in the draft after participating in the G League elite prospect camp last month.
"I felt like in college I wasn't getting enough opportunity. I wasn't feeling like myself in college," he said. "[The invite] kind of opened a lot of doors for me. ... I feel like it really brought me back and kind of showed a little bit what I can do. And once I started getting calls from teams to work out, I was like, 'Man, this is what I want to do.' I mean I'm here, it's right in front of me, so just go for it. So I continued to work."
The decision didn't go over well with his father, however.
"He didn't like that idea at all," O'Neal said. "It sucks that he didn't like that idea, but I'm a grown man, I'm 22 years old, I can make my own decisions. It was right in front of my face. I'm not backing up from it. I'm going to go get it if I see it. That's just how I'm built. I take everything the same way. I took my heart surgery the same way. Being cleared was right in front of me, being healthy was right in front of me, and I went for it. I'm not backing down from nobody. I know he's an NBA legend, I know he's my dad, but it was right in front of me, I had to go get it. So, if he likes it or not, it's not really going to stop me from doing what I want to do."
The Lakers do not hold any picks in the draft Thursday -- no first- or second-rounders -- but have still hosted a handful of draft workouts the past couple of weeks to see prospects up close. They hope to be able to buy a pick Thursday night and are interested in adding young talent that goes undrafted, like they did with Austin Reaves last season, sources told ESPN.