Both players are currently asymptomatic and in quarantine under the care of the team's physician.
"All players and members of the Lakers staff are being asked to continue to observe self-quarantine and shelter at home guidelines, closely monitor their health, consult with their personal physicians and maintain constant communication with the team," the team said in a statement.
The Lakers players, whose names were not reported, were administered tests Wednesday at the team's practice facility in El Segundo. On Wednesday, a majority of the Lakers players were tested for COVID-19, according to the Los Angeles Times.
Per The Athletic, the team may now administer tests to the remaining players who did not take tests Wednesday morning.
Mere minutes after Charania's report broke, the Boston Celtics announced one of their players had tested positive, too.
The news comes just days after the Nets announcing that four players, including star forward Kevin Durant, had tested positive for COVID-19.
When the Lakers hosted the Nets on March 10, the NBA had recently enacted new social distancing guidelines, including only allowing essential team personnel into locker rooms and keeping a six-to-eight foot distance from reporters.
Including the two Lakers and Boston Celtics guard Marcus Smart, who announced he contracted the coronavirus on Thursday evening, there are now 10 known NBA players who have tested positive for the coronavirus.
Earlier Thursday, both the 76ers and Nuggets announced that members of their respective organizations also tested positive.
The NBA suspended the season indefinitely last Wednesday after Jazz center Rudy Gobert preliminarily tested positive. He was the first NBA player to do so.
ESPN's Adrian Wojnarowski previously reported that NBA owners and executives have discussed a possible best-case scenario for teams to return to play by mid-to-late June, likely with no fans at games.
NBA commissioner Adam Silver said Wednesday that he's optimistic that the season in some form could be salvaged, but did not have an idea regarding timing.
"When public health officials give us the okay," Silver said.
NBA teams' access to coronavirus tests have been an increasing subject of speculation, as many hospitals lack an adequate number of tests. Following the announcement that a number of Nets players tested positive, New York City mayor Bill de Blasio crafted a critical tweet about the subject, stating, "Tests should not be for the wealthy, but for the sick."
In response, NBPA executive director Michele Roberts defended the league for getting access to tests for its players.
"The problem that more of us can't get the tests—and I'm not apologetic about saying it—in my view, that rests at the foot of the federal government," Roberts said. "They were responsible for making sure we were protected in that regard and I think they failed."
As of Thursday evening, there are more than 233,000 confirmed cases worldwide, causing nearly 10,000 deaths. There are more than 10,800 confirmed cases of COVID-19 in the United States.