The fabled franchise is widely believed to have a long list of potential candidates earmarked for interviews after Mike D'Antoni resigned two days ago following a woeful 27-55 record.
Among the leading contenders are Byron Scott, Kurt Rambis, George Karl and Jeff Van Gundy, as well as heavyweight college coaches Kevin Ollie of Connecticut and Kentucky's John Calipari.
The Lakers, however, are keeping their cards close to the chest.
Asked if the team had an official list of potential candidates, Lakers vice president of public relations John Black told Reuters on Friday: "No, we would not do something like that."
Scott and Rambis are both former Lakers players and have previously worked as head coaches in the NBA, Scott for 13 years and Rambis with the Minnesota Timberwolves from 2009 to 2011.
Rambis, 56, would be an extremely easy fit as he has served three separate spells as an assistant coach with the Lakers, most significantly under the esteemed Phil Jackson for seven seasons.
Veteran Karl, who in December 2010 became the seventh coach ever in the NBA to record 1,000 wins, would be an interesting choice given that his son, Coby, played for the Lakers during the 2007-08 season.
The 62-year-old Karl most recently coached the Denver Nuggets before being fired in June 2013, having led the team into the playoffs for each of his nine seasons in charge.
Van Gundy, head coach with the New York Knicks from 1996-2001 and Houston Rockets from 2003-2007, has been linked with the Lakers as a potential candidate in the past but neither party ever came close to reaching a deal.
Hiring a college coach would break new ground for the Lakers and Calipari is widely regarded as a permanent fixture in Kentucky, having guided the team to the Final Four in 2011, 2012 and again this year.
Ollie, 41, would be an interesting proposition having played for 12 different teams during his lengthy NBA career before becoming head coach with Connecticut and leading them to the 2014 NCAA men's championship title.
When D'Antoni's resignation was announced by the Lakers on Wednesday, general manager Mitch Kupchak said the search for a replacement would begin immediately, though no timetable had been established.
The team will undoubtedly come under intense pressure to find an ideal candidate after frustrating Lakers fans with their last two choices.
Jackson's departure in 2011, after leading the club to five NBA titles during his two spells at the helm, was followed by the unsuccessful appointments of Mike Brown and then D'Antoni.
Brown was sacked after a dismal 1-4 start to the 2012-13 campaign and D'Antoni finally departed after compiling a 67-87 record over two seasons.
Granted, both Brown and D'Antoni always faced a near-impossible task as the first two successors to Hall of Fame coach Jackson but the Lakers, as 16-time NBA champions, are held to a lofty standard by their supporters.
The D'Antoni era was especially frustrating for die-hard fans as he agreed to a three-year deal in November 2012 despite the fact that the ever popular Jackson was considering a third spell in charge.
Under D'Antoni's offense-minded but small-ball approach, the Lakers continually mis-fired and, amid a bewildering array of injuries, they plunged embarrassing new depths as they finished the 2013-14 regular season well under .500.
Never before had they lost so many games in a single campaign, and they were eliminated from playoff contention in March.
At home, they were a dismal 14-27 in front of Staples Center crowds who became bored and gradually dwindled in number and the team failed to reach the playoffs for the first time since 2005, and only the sixth time ever.
D'Antoni came under increased criticism for his various strategies during the season and did not always communicate well with his players, though a rash of injuries certainly made his job a lot more difficult.
Whoever replaces D'Antoni as head coach faces a daunting task in restoring the team to the giddy heights they once took for granted, and thereby regaining the faith of the fans.
Twelve of the Lakers' 15 players are expected to be free agents in July, and the team is unlikely to have a head coach in place before the May 20 draft lottery.