They want to set up meetings with the high-powered free agents, even though the battle is more uphill than anything against two powerful opponents — the Miami Heat and Phil Jackson.
The Lakers are leery that James will return Miami but they still want the chance to meet with him and pitch themselves as perennial championship contenders.
They also hope to sit down Thursday with Anthony but realize Jackson, the new president of the New York Knicks, will probably get the final meeting with the high-scoring small forward.
Anthony would have made $23.3 million and James would have made $20 million next season. The Lakers are currently about $22 million under the projected salary cap of $63.2 million.
Meanwhile, Pau Gasol started looking at new teams for the first time since February 2007, narrowing his interests to Golden State, Oklahoma City and Chicago. The Lakers are a possibility for him, though he has said he wants to play for a championship-caliber team. The Lakers went 27-55 last season.
Gasol, who turns 34 on Sunday, made $19.3 million last season.
The Lakers also expressed interest in someone from their more distant past — Trevor Ariza.
He was deadly accurate from three-point range in the Lakers' 2009 championship run but left immediately for a five-year deal with Houston. He has since played for New Orleans and Washington and last season averaged 14.4 points while shooting a career-best 40.7% from three-point range for the Wizards. Ariza, who turned 29 Monday, made $7.7 million last season.
And they also called the agent for Nick Young, who averaged a career-high 17.9 points for the Lakers last season and became a free agent by declining a player option that would have been worth $1.2 million next season.
Randle arrives in L.A.
Julius Randle's introductory news conference started 27 minutes late, the result of medical testing that ran long at the Lakers' training facility and also his desire to return to a nearby hotel to clean up for local media members.
It wasn't long, though, until he gave everybody some sound bites Monday morning in El Segundo.
The power forward from Kentucky showed that the Lakers drafted a personality in addition to potential with the seventh overall pick last Thursday.
A lifelong Lakers fan despite growing up in Dallas, Randle is well aware of what it means to play with Kobe Bryant.
"I've been warned," he said, pausing dramatically amid laughter from reporters. "I've been told he can push his teammates."
When Randle can start pushing people in the post remains to be seen.
His right foot was surgically repaired when he was in high school, and the Lakers are deciding whether he should have a screw removed from it before his NBA career begins.
"For the next two or three days, we're going to continue with the physical process," General Manager Mitch Kupchak said. "Based on his performance and his play last year through a full schedule, we don't expect anything different to come up."
Randle will wear No. 30 with the Lakers, a number he borrowed before his Kentucky career from his mother, Carolyn Kyles, who played at the University of Texas-Arlington.
She once told him, "If you're going to wear it, you've got to do something with it," Randle said. "Playing for the Lakers, I guess I've [done] something."
Times correspondent Eric Pincus contributed to this report