Lue, 41, led the Cavs to an NBA Finals championship and three Eastern Conference titles from 2015-2018. Cleveland went a combined 169-103 in the regular season and playoffs under Lue.
He played for the Lakers from 1998-2001 and was a part of two NBA championship teams in L.A.
Williams, 47, has five years of NBA head-coaching experience; he led the New Orleans Hornets/Pelicans from 2010-2015. He led New Orleans to two postseason appearances and amassed a 175-229 record.
Both men appear to be the favorites to replace Luke Walton, who mutually parted ways with the franchise on Friday after three seasons at the helm. On Saturday, Walton reportedly agreed to become the new head coach for the Sacramento Kings, per Adrian Wojnarowski of ESPN.
Wojnarowski in particular called Lue a "strong frontrunner" for the gig.
Lue has a connection with Lakers superstar LeBron James, who played on the Cavs during all but six games of his head-coaching tenure.
James and Lue got along well, as evidenced by the player's remarks following his former coach's firing after a 0-6 start this season:
"He put us in position to win, he put us in position to succeed," James said. "And more importantly, he gave—all the onus was on the players. He gave us the responsibility to go out and do what we needed to do to win ball games. And that led us to—while he was at the helm—three Eastern Conference Finals, three Finals, one championship."
Williams coached Davis for three seasons in New Orleans. The two were clearly close:
The Associated Press also said Williams had a "strong relationship" with Davis when the coach was fired in 2015.
Davis requested a trade on Jan. 28. One did not materialize before the Feb. 7 deadline, but he can become a free agent after next season and could conceivably sign with the Lakers even if the Pels decide to trade him elsewhere. Hiring Williams could be a selling point for Davis and ease his transition to the team should he don the purple and gold.
The next Lakers head coach will be the team's sixth this decade.