UCLA’s Lonzo Ball, right, with his father, LaVar, after a game in March. (Mark J. Terrill/Associated Press)

The Lakers have the No. 2 pick in June’s NBA draft, and with the Celtics expected to take Washington’s Markelle Fultz at No. 1, Los Angeles has to make a franchise-altering decision: go with UCLA’s Lonzo Ball, a local product widely viewed as the second-best option to Fultz, or go with … someone else.

The Lakers could pass on Ball if they determine that he doesn’t suit their roster, if they see too many flaws in his game or if they simply like another player better. Of course, another reason they might pass on Ball is because of his rather infamous father.

Since the spring, LaVar Ball has leveraged his son’s burgeoning fame and his own talents for making outlandish boasts and provoking high-profile feuds into major sports-celebrity status. Along the way, he’s made all too clear that he a) fully intends to be a major, if not domineering, presence in the lives of all his children and b) strongly wants Lonzo to play for the Lakers.

“That’s all we working out for is the Lakers,” Ball said shortly after Wednesday’s draft lottery. “Just the Lakers. There’s nobody else that we need to work out for.”

For their part, the Lakers, not to mention other NBA teams, could be concerned that drafting Lonzo Ball essentially means bringing aboard his loudly opinionated father, as well. That was behind the question Dan Patrick posed to Luke Walton on the former’s radio show Friday, regarding whether the Lakers Coach would ask UCLA Coach Steve Alford about LaVar Ball’s “involvement” with the Bruins’ program this past season.

“I wouldn’t personally, but yes, somebody in our organization will,” Walton replied. “Absolutely.”

Asked if LaVar Ball’s possible level of meddling with UCLA was “a topic of discussion” for the Lakers, Walton said, “Not yet,” adding that the subject might surface as the draft draws closer. “I’m mostly concerned with what player can help us win more than 26 games the most,” Walton said with a chuckle.

The elder Ball has been a contentious figure at the high school where Lonzo starred and where his two younger sons, LiAngelo and LaMelo, are current standouts (and, the father insists, future Bruins). His family has helped lead that Los Angeles-area program, Chino Hills, to undefeated runs and state championships, but Ball has been accused of undermining the authority of the coaches.

In one incident reported by For the Win, Ball was contradicting the Chino Hills head coach’s instructions during a game, then refused to leave the team’s locker room afterward, despite the coach asking him to do so. Later that evening, at the team’s hotel, Ball reportedly gathered the team without the coach’s permission and was heard yelling, “I run Chino Hills! I run UCLA, about to run the NBA!”

After UCLA was ousted from the NCAA tournament by Kentucky, Ball told a reporter that the Bruins — and his son in particular — would have had more success, except that they featured “three white guys.” He later said his words were misinterpreted, adding, “I love those guys,” although his specific praise for the three players in question was that they were “nice” and “respectful.”

After Alford shot down rumors that he might leave UCLA to coach his alma mater, Indiana, Ball said, “I feel good about that. He knows my boys. I like his style, and I’m glad he’s staying.”

“I think what you’re drafting is the son and not the father,” Lakers team president Magic Johnson said last week. “I think that you also are gauging and evaluating his son on his ability and what he can do not only on the basketball court, but also what he can do for your team. How he can enhance and make your team better.”

Walton told Patrick he thought Lonzo Ball was “an unbelievable player,” saying, “I absolutely love his game, and the way he passes, the way he makes everyone on his team better. It’s an unbelievable skill, it’s a joy watching him play.”

“I think, right now on paper, he’s a great fit,” Walton continued, “but the reality is there’s a lot of really talented kids in this draft.”

The coach said that, in addition watching game film of its draft prospects, Los Angeles would “dive into what they’re like,” including “how they treated the managers on the team” and how diligent they were about getting treatment for their injuries. “When you talk about draft picks this high, there’s going to be a lot of research done,” Walton said. “So that’ll play into who we draft, as well.”