James last missed the play-offs in 2005 and has appeared in the NBA Finals in each of the last eight seasons.
He scored 31 points and had 10 assists on Friday night but it was not enough to prevent the Lakers losing for the third time in four games.
The latest loss leaves the Lakers four wins back on the San Antonio Spurs, who lie in the eighth and final play-off spot in the Western Conference.
Eric Bledsoe scored 31 points for the Bucks, who top the Eastern Conference, while MVP candidate Giannis Antetokounmpo had 16 points and 15 rebounds.
It took four overtime periods to separate Chicago and Atlanta before the Bulls prevailed 168-161.
Zach LaVine scored a career high for the second time this week, finishing with 47 to beat his previous best of 42, to help settle the third-highest combined scoring game in NBA history.
Hawks rookie Trae Young's hit a milestone of his own with a career-high 49 points but it was not enough to lift his side over their Eastern Conference rivals.
In Boston, the Celtics stopped a four-game losing run by beating the Washington Wizards 107-96.
Marcus Morris top-scored with 17 points and nine rebounds, while Marcus Smart scored 16 points and Kyrie Irving added 13 as seven Celtics players finished with a score in double figures.
In the night's other games, the Toronto Raptors edged the Portland Trail Blazers 119-117, the Charlotte Hornets beat the Brooklyn Nets 123-112, the New Orleans Pelicans overcame the Phoenix Suns 130-116 and the Los Angeles Clippers secured a 116-109 victory over the Sacramento Kings.