Brown, who originally went through training camp with the team but was cut before the regular season, was signed March 10 on an initial 10-day contract.
Through four appearances with the team, Brown averaged 7.0 points a game while shooting 57.9% from the field.
After his second $29,843 contract expires, following the Lakers' visit to the 76ers in Philadelphia on March 30, the team will either re-sign him for the remainder of the season or let him go to free agency.
The Lakers' total salary for the season is now $70.3 million. With four players out for the season (Kobe Bryant, Ronnie Price, Steve Nash and Julius Randle), the Lakers have been given a hardship exception by the NBA to sign Brown as a 16th player -- one greater than the standard roster maximum of 15.