LeBron James (37) reached 31 points, 8 rebounds and 8 assists but missed the last shot that would have sent the game to overtime.
Center Anthony Davis (31), their other star, scored 22 points, 10 rebounds and 6 blocks but the Lakers were weighed down by another mediocre game from Russell Westbrook (33) (10 points on 4/15 shooting) and the lack of support from their bench.
After failing to make the playoffs last season, the Lakers have yet to get back on track during this dismal start to the season.
The Los Angeles team, who fired coach Frank Vogel but made only minor changes to the roster, have already lost to the Warriors, to their neighbours, the Clippers, and now to the Blazers, who have three wins since Lillard's return from injury.
The Crypto.com Arena crowd watched in frustration as erratic moments like LeBron James' near mid-range shot that missed the rim and Westbrook's rash mid-range shot missed with 27 seconds left.
Westbrook's miss, the main target of criticism against the Lakers, irritated both their fans and LeBron James himself, who had not yet joined the attack and had to turn around with gestures of frustration.
The Lakers got to an 8-point lead (98-90) with four minutes left but Lillard cut into the lead with 7 straight points and then nailed a spectacular three-pointer to put the Blazers ahead 104-102 with just 12 seconds left on the clock.
James tied it on the next action but, after a Jerami Grant basket for Portland, he gambled on the final possession with a risky shot diving backwards that didn't go in and sealed the visitors' win.
Westbrook in the crosshairs
The Lakers now have a few days off before trying to end their losing streak on Wednesday against the Denver Nuggets.
The Los Angeles team has exhibited problems in all facets of the game but mainly in shooting, with a mediocre percentage of 21.2% in three-pointers.
The biggest issue is Westbrook, NBA MVP in 2017 and collecting a salary of $47 million this season, whose performance has collapsed in Los Angeles to average in these first three games: 10.3 points on 28% shooting from the field and 8.3% in three-pointers (1 of 12).
After the loss, LeBron James tried to dodge questions about his teammate's poor decisions late in games.
"I'm not here to do that (...) We just didn't put them in," the forward said about the shots down the stretch.
"Westbrook "had some good shooting positions but couldn't put them in. Defensively, we couldn't stop them on several actions. And Dame (Lillard) was strong down the stretch."
Other NBA results:
Golden State Warriors - Sacramento Kings 130-125
In other games, the Golden State Warriors beat the Sacramento Kings by a tight 130-125 after scoring an overwhelming 89 points in the first half.
The reigning champions built a 26-point lead but let the Kings dream of a comeback.
Point guard Stephen Curry (34), who scored 28 points and six three-pointers in the first two quarters, finished the night with 33 points.
New Orleans Pelicans - Utah Jazz 121-122
The New Orleans Pelicans, meanwhile, fell 122-121 to the Utah Jazz in overtime and are also on edge due to the physical condition of their two stars, Zion Williamson (22) (25 points) and Brandon Ingram (10), who had to leave the game with injuries.
Williamson, who just made his comeback after a season sidelined by a foot injury, suffered a jarring backward fall when he jumped for a dunk and Jordan Clarkson blocked him.
Center Kelly Olynyk, with an acrobatic layup with three seconds left, gave the victory to the Jazz, undefeated with three wins despite shedding their two big stars, Rudy Gobert and Donovan Mitchell, in the summer.
Cleveland Cavaliers - Washington Wizards 117-107
Donovan Mitchell (26) scored 37 points to lift host Cleveland to an overtime victory over Washington.
Mitchell has a franchise-record three straight games of at least 30 points to start the season. Cedi Osman scored 16 points off the bench and Jarrett Allen collected 15 points and 14 rebounds for the Cavaliers, who played their second straight game without All-Star guard Darius Garland (eye).
Bradley Beal scored 27 points and Kristaps Porzingis added 18 points and 11 rebounds for the Wizards, who sustained their first loss of the season.
Atlanta Hawks - Charlotte Hornets 109-126
Short-handed Charlotte got a career-high 20 points and 11 rebounds from Nick Richards (24) as they beat hosts Atlanta.
Richards was one of six players to score in double figures for the Hornets, who were playing without leading scorer Terry Rozier (right ankle sprain), Cody Martin (left quad soreness) and LaMelo Ball (left ankle sprain). The Hornets also got 24 points and 10 rebounds from Kelly Oubre Jr. and 18 points from Dennis Smith Jr.
Atlanta was led by Trae Young with 28 points and nine assists and Dejounte Murray with 19 points and eight rebounds.
Oklahoma City Thunder - Minnesota Timberwolves 106-116
Anthony Edwards (21) scored 30 points and grabbed 11 rebounds to lead Minnesota over host Oklahoma City.
Rudy Gobert added 15 points and 15 rebounds for Minnesota, while Karl-Anthony Towns also scored 15. Gobert was 7-for-8 from inside the arc.
The Thunder were without leading scorer Shai Gilgeous-Alexander, who suffered a hip contusion late in Saturday's loss to Denver. Luguentz Dort led the Thunder with 20 points, but was just 6 of 15 from the field. Jeremiah Robinson-Earl added 15 points.
LA Clippers - Phoenix Suns 95-112
Devin Booker (25) scored 35 points and Chris Paul added 11 assists against his former team as visiting Phoenix earned a victory over Los Angeles.
Deandre Ayton added 13 points for the Suns, who led by as many as 22 while bouncing back from an overtime defeat at Portland on Friday. Marcus Morris Sr. scored 22 points and John Wall added 17 for the Clippers.
With his first two assists of the game, Paul reached 11,000 for his career. The milestone pass led to an alley-oop dunk by Ayton as Paul became the first player in NBA history with at least 20,000 points and 11,000 assists.
