The meeting went "really well," a source who was in the room for the Lakers' presentation told ESPN.com's Ramona Shelburne.
"LaMarcus seemed completely focused," a source told Shelburne.
The Lakers' contingent included Kobe Bryant, president Jeanie Buss and general manager Mitch Kupchak.
The Houston Rockets met with Aldridge after the Lakers.
According to one source, the chance of Aldridge staying with the Portland Trail Blazers is "very unlikely."
ESPN.com reported in May that the Spurs and Mavericks strongly believe they'll have a great shot to lure Aldridge back to his home state of Texas. But sources said last week that Aldridge is actually thinking more and more about a free-agent jump to the Lakers.
The Lakers, sources added, firmly believe they will now be in the Aldridge hunt. And there is a rising sentiment, sources said, that the Lakers have edged past the Mavericks on Aldridge's wish list even though he was a high school star in Dallas.
The Spurs, sources say, continue to be Aldridge's most likely destination if he goes through with the idea of leaving the Blazers to start anew.
After the meeting, sources said Lakers coach Byron Scott, COO Tim Harris and Kupchak flew to Washington D.C. to meet with Greg Monroe on Wednesday. They will then return to Los Angeles to meet with DeAndre Jordan.
ESPN.com's Marc Stein and ESPN The Magazine's Chris Broussard contributed to this report.