"Today's group are not players that we're considering for the second pick in the draft, but there's a lot of players we'd consider at 27 and 34," said General Manager Mitch Kupchak, referring to the team's other two picks.
The team put Northern Iowa's Seth Tuttle, Minnesota's Maurice Walker, Gonzaga's Kevin Pangos, Arizona's T.J. McConnell, Maryland's Dez Wells and Iowa State's Bryce Dejean-Jones through their paces.
The Lakers got a big win when they jumped from fourth to second in the NBA's draft lottery.
"Our roster looks better, clearly, after getting the pick in the lottery last Tuesday," said Kupchak. "You know you're going to get a really good player. You're going to get a player that you're going to be able to control for at least five years, at a reasonable amount, before you have to consider an extension."
The Lakers won just 21 games this season, the lowest total in franchise history.
"Being able to put the season behind us and having something positive to show for it is a good thing," said Kupchak, although he's not sure the Lakers will keep all three of their picks in the draft.
"We don't know if we're going to draft three players," he said of the team's two later selections. "We may draft a player who might have to wait a year or two in Europe."
Kupchak also said the team would bring in four to eight players over the coming weeks who are under consideration for the Lakers' No. 2 pick.
"There's the conception that there's four players there. I think there might be more," said Kupchak, probably referring to Duke's Jahlil Okafor, Kentucky's Karl-Anthony Towns, Ohio State's D'Angelo Russell and Emmanuel Mudiay, who played in China last season.
He also noted that the Lakers could trade their first-round pick, although Kupchak said the price would be significant.
"Nothing's really taken place in that regard. It would have to be a heck of an opportunity for us to consider something like that," Kupchak said. "We're a little bit impatient, so if you came across something that made you better quicker ...."
Meanwhile, the team held workouts for six second-round prospects on Tuesday.
"It was fun," said the 22-year old, 6-foot-8 Tuttle. "Any time you get to play in front of the Lakers or in this building it's quite an experience."
Tuttle envisions himself as a versatile stretch power forward, but he's willing to do whatever is needed to fit in with a team.
Walker, a 23-year-old, 6-10 forward/center, said he's more of a "back-to-the-basket scorer."
Wells, who worked out previously with the Boston Celtics, considers himself a "jack of all trades."
"I can play both sides of the floor, can score, can defend, make the right plays, rebound," said Wells, a 6-foot-3, 23-year-old shooting guard. "I can do some of everything"
Point guard Pangos was a teammate of current Lakers center Robert Sacre at Gonzaga.
"He was like a big brother to me in my first season, really showed me the ropes, just a great dude," said the 22-year old Pangos, who is happy he stayed with the Bulldogs for four years.
"I'm more ready than ever right now to move on to that next step. After the first three years, I don't think I'd be as good as I am now," he said.
McConnell, who has also auditioned for the San Antonio Spurs, is eager to prove that he can hit the outside shot.
"I think if I show I can knock down the three-point shot, that will elevate my game," said the 6-foot-2 point guard.
Dejean-Jones, a 6-foot-6 shooting guard who played locally at Taft High School, averaged 10.5 points and 4.7 rebounds a game for the Cyclones.
The Lakers will hold a similar workout, primarily for prospects for their lower two picks, on Thursday.