James swapped the Cleveland Cavaliers for the Lakers in 2018-19 but he was unable to lead the storied NBA franchise to the playoffs.
The 34-year-old averaged 27.4 points, 8.5 rebounds and 8.3 assists for the Lakers, who missed the postseason for the sixth successive season.
James, who also struggled with a groin injury that limited him to 55 games, failed to make the playoffs for the first time since 2004-05.
Jefferson, who played alongside James for the Cavaliers from 2015-17, backed the three-time champion and four-time MVP to bounce back in a big way.
"LeBron James will be the best player in basketball next year, again," Jefferson told ESPN's 'Get Up!' on Monday.
"Now, will he be the LeBron James from '08 and chasing down blocks? No. But, he's going to do so many different things. … I think he understands the disrespect. He's felt it over the course of his career, at different levels. Now, it's like 'Oh, you're old. You're not that guy anymore'.
"But, I think, really and truly, he's more focused on proving to people that basketball is the most important thing to him. And, the only way to do that is to go and destroy as many people as possible."
The Lakers' roster should be much improved this season after they acquired Anthony Davis from the New Orleans Pelicans in exchange for Lonzo Ball, Josh Hart, Brandon Ingram and three first-round picks this offseason.
Los Angeles had cap space to add a third star next to James and Davis, but missed out on Kawhi Leonard, who joined cross-town rivals the Los Angeles Clippers.
The Lakers then signed Avery Bradley, Danny Green, Kentavious Caldwell-Pope, JaVale McGee, Quinn Cook, DeMarcus Cousins, Rajon Rondo and Alex Caruso to deals.