The Lakers also made it clear to Anthony they'd offer him a maximum four-year, $95 million contract if he chose to sign with them, according to sources.
Anthony arrived at the team's practice facility shortly after 3 p.m. ET, and departed just before 6 p.m.
Escorted to his car by Lakers general manager Mitch Kupchak on the way out, Anthony stopped to say hello to reporters and signed autographs for Lakers fans but declined to comment on the meeting.
"You know I can't say anything right now, but I wanted to stop and say hey," Anthony said.
A person who was in the Lakers' pitch said they thought it went "really well" and added, "I don't know how big of a shot we have, but I think we have a shot."
Another Lakers source described Anthony as "extremely attentive" throughout the meeting.
While Anthony was told that a max offer would be his for the taking if he wanted it, the Lakers also discussed scenarios in which he and James could both come to the Lakers and how much money each would earn in doing so, a league source said.
Anthony was flanked by agent Leon Rose and business manager Bay Frazier as the group was greeted in the parking lot by former Lakers great James Worthy and then escorted into the building for the beginning of the meeting.
Kobe Bryant was not able to make it back from a family vacation in Europe in time for the meeting, according to sources. Bryant intended to meet with Anthony later Thursday evening, after Anthony's meeting with the New York Knicks following his session with the Lakers, sources said.
Bryant reached out to Anthony directly to explain why he wasn't able to make the meeting, after the time had been moved up, sources said. The two are close friends, and have been in touch throughout the entire process.
The Lakers' presentation was led by team president Jeanie Buss, executive vice president of player personnel (and Jeanie's brother) Jim Buss and Kupchak. It also included Lakers chief operating officer Tim Harris and executives from Time Warner Cable SportsNet, the Lakers' television network, and representatives from AEG.
Movie producer Joel Silver was also present and created a short film in homage to Anthony, followed by a conversation about the avenues that Anthony and his wife, La La Vasquez, can take into the entertainment industry, multiple sources told ESPNLosAngeles.com.
The Lakers intended to sell Anthony on their championship tradition, commitment to winning and unique platform as the glamour franchise of the NBA, with the largest profit margins available to pour back into the team.
After the Jeremy Lin kerfuffle in Houston on Wednesday, when the Rockets displayed digital images of Anthony wearing Lin's No. 7 jersey on the side of the Toyota Center even though Lin is still under contract, L.A. had a No. 7 Lakers uniform mocked up for Anthony as part of the presentation, according to a source, but did not make any grandiose gestures like the billboard campaign the Lakers did last summer to try to get Dwight Howard to stay with the team. The Lakers chose to believe Anthony's main focus is on winning and not fame.
Xavier Henry wore No. 7 for the Lakers last season, but he is currently a free agent.
Anthony's free-agency choice isn't expected to come immediately.
After meeting with the Knicks later Thursday, Anthony did not give them an answer or a timetable for his decision, a source told ESPN The Magazine's Chris Broussard. He will take the long weekend to think things through, the source said.