The victory gives the Trail Blazers the head-to-head tiebreaker if the two clubs finish with identical records at season's end.
Lillard shot 12-of-18 from the field and 9-of-9 from the charity stripe en route to his 31st 30-point game of the campaign. Backcourt mate CJ McCollum added 21 points and four assists.
Lakers star Anthony Davis had his best performance since his return from a calf injury. The former No. 1 overall pick finished with 36 points, 12 boards, five assists, and one block.
"I feel good. I feel like I'm getting my legs back under me," Davis told reporters postgame, according to Spectrum SportsNet's Mike Trudell.
LeBron James sat out his third consecutive game to nurse a sore right ankle. The 36-year-old is reportedly aiming to return either Tuesday against the New York Knicks or Wednesday vs. the Houston Rockets.
Portland now owns a one-game lead on Los Angeles for the West's No. 6 seed.
The Lakers have lost eight of their past 11 games.