According to a team spokesman, the Lakers auditioned 11 players outside the view of the media, in addition to the 72 candidates who worked out publicly, as the franchise prepares to select second, 27th and 34th in the draft on Thursday.
Looney, a 19-year-old, 6-foot-9 freshman, projects to be a first-round pick after averaging 11.6 points, 9.2 rebounds and 1.3 steals a game for the Bruins.
Upshaw was one of the best NCAA defenders, averaging 10.9 points, 8.2 rebounds and 4.5 blocks through 19 appearances with the Huskies.
The 21-year-old 7-footer was dismissed from the team for violating team rules, reportedly for failing drug tests. He was previously left Fresno State under similar circumstances.
According to website DraftExpress.com, Upshaw may also have a heart-related medical issue.
The Lakers also auditioned eight other prospects over the past few weeks, including Oklahoma State forward LeBryan Nash, Ohio State guard Shannon Scott, Cal State Northridge guard Stephan Hicks, St. Bonaventure center Yousou Ndoye, Minnesota guard Andre Hollins, Washington State guard DaVonte Lacy, San Diego State forward J.J. O'Brien and Boise State guard Derrick Marks.
The team's official count is 83 prospects.
While the Lakers didn't confirm it, Iowa center Gabe Olaseni was also brought in to play against Duke center Jahlil Okafor, according to a person familiar with the workout but not authorized to speak on the record.
Guards D'Angelo Russell (Ohio State) and Emmanuel Mudiay (who played in China last season) both worked out twice for the Lakers -- as did Okafor.
UCLA guard Norman Powell said he was scheduled for a second audition with the team on Wednesday.
The Lakers previously disclosed a private workout with Latvian forward Kristaps Porzingis.