James moved to the Lakers after completing a second spell with the Cleveland Cavaliers last summer.
But the Lakers have struggled without the 34-year-old, who has missed 17 games through injury this season, to miss the play-offs for a record sixth straight year.
James, who last failed to make the play-offs in 2005, finished with 25 points, 14 assists and nine rebounds, but it was Nets guard D'Angelo Russell who stole the show on Friday night.
Russell, traded away by the Lakers after two years in 2017, had 21 points and 13 assists, while Joe Harris scored a team-high 26 to condemn the Lakers to another defeat.
Elsewhere, Giannis Antetokounmpo came back from a two-game absence to fire Milwaukee Bucks to a comfortable win over Miami Heat.
Antetokounmpo, recently sidelined with a sprained right ankle, returned to devastating effect, scoring 27 points, with eight rebounds and seven assists in a 116-87 victory.
At the Scotiabank Arena, Oklahoma City Thunder came from 13 points behind to beat the Toronto Raptors and end a four-game losing streak.
Russell Westbrook starred for the visiting side with his 28th triple-double of the campaign, as he concluded the evening with 18 points, 12 rebounds and 13 assists.
Paul George (28 points) and Dennis Schroder (26) were also on song for the Thunder.
James Harden equalled career-best figures as he helped Houston Rockets beat the San Antonio Spurs at the Toyota Center.
Harden delivered with 61 points, a feat he also managed at the New York Knicks in January, to secure a 111-105 win.
It marked Harden's second consecutive 50-point game, and a remarkable eighth of the campaign.
In the night's other matches, Nikola Jokic scored 21 points as Denver Nuggets secured a 111-93 win over the New York Knicks, while Orlando Magic recorded a 123-119 victory against the visiting Memphis Grizzlies.
Danilo Gallinari scored 27 points as the Los Angeles Clippers won 110-108 at the Cleveland Cavaliers.