The two sides had reached an impasse following discussions over his contract, league sources told ESPN's Adrian Wojnarowski.
Lue reportedly turned down a three-year, $18-million offer after seeking a five-year contract with an appropriate salary for his championship resume. A three-year pact would have coincided with the remaining years of LeBron James' contract.
The Lakers were hopeful that former Milwaukee Bucks head coach Jason Kidd would come aboard as part of Lue's staff, according to Wojnarowski. Kidd reportedly made a strong impression during his interview with general manager Rob Pelinka and advisor Kurt Rambis, with tremendous value being placed on his tenure in Milwaukee and his work with the team's young players.
Rambis reportedly has been given a sizable role during the Lakers' head coach search.
Lue won over the Lakers with his high basketball IQ and approach to how he'd coach the current roster, according to Wojnarowski. His relationship with James was also considered a plus.
James informed the Lakers he trusts their judgment and doesn't want to be involved in the hiring process, league sources told The Athletic's Shams Charania.
Lue led the Cavaliers to a record of 128-83 across four seasons before he was canned six games into the 2018-19 campaign following an 0-6 start. Cleveland advanced to the Finals on three occasions and captured the 2016 championship with Lue on the sidelines.
The Lakers haven't reached the playoffs since 2013.