Lue's first interview was last Friday in Newport Beach with general manager Rob Pelinka.
The interview Wednesday will be with Lakers owner Jeanie Buss, as well as a second chat with Pelinka.
Lue led the Cavaliers to a championship as their coach in the 2016 season. He is the only coach in NBA history to lead a team back in the Finals from down 3-1.
The 41-year-old took over the Cavaliers midway into the 2015-16 season, leading them to a NBA title.
The following two seasons the Cavs went a combined 101-63, losing in the Finals both seasons to the Golden State Warriors.
Overall with Cleveland Lue went 128-83.
Lue was fired this past season by Cavaliers owner Dan Gilbert as the team went 0-6 to begin the season.
He also was on the Lakers' roster as a reserve in both 2000 and 2001 -- years the team won championships.
The Times reports that along with Lue, the Lakers are interested in Miami Heat assistant Juwan Howard and plan a second interview with Philadelphia 76ers assistant Monty Williams.
The Lakers and coach Luke Walton parted ways two days after the end of the regular season.