According to ESPN.com's Chris Haynes, Allen feared Lillard would request a trade, but the 27-year-old point guard instead made it clear that he has championship aspirations in Portland.
The meeting reportedly occurred prior to a 100-86 home win over the Indiana Pacers last week.
Per Haynes, Lillard wanted to use the meeting to both tell Allen he is committed to the Blazers and to make sure Allen is taking the necessary steps to make Portland a championship contender moving forward.
A source told Haynes that the meeting took place without the knowledge of anyone else in the organization.
In addition to Lillard and Allen discussing what may be needed in order to get the team over the top, Lillard reportedly gave head coach Terry Stotts a vote of confidence.
At 25-22, the Blazers are seventh in the Western Conference and hold a 1.5-game lead over the ninth-place Los Angeles Clippers.
Portland has reached the playoffs in each of the past four seasons, and while it has made it to the second round on two occasions during that time, it has been unable to to break through with a Western Conference Finals or NBA Finals appearance.
Lillard is enjoying another strong individual season, with 25.2 points, 6.6 assists and 4.8 rebounds per game.
He has been the Blazers' unquestioned go-to player since forward LaMarcus Aldridge signed with the San Antonio Spurs prior to the 2015-16 season.
Shooting guard CJ McCollum has developed into a solid wing man for Lillard, with 21.4 points per game, and center Jusuf Nurkic has been productive as well.
Portland is somewhat lacking in terms of top-tier talent otherwise, and it likely will need to make additions in order to compete with the likes of the Golden State Warriors, Houston Rockets and San Antonio Spurs in the Western Conference.