The 32-year-old guard, who helped Boston capture the 2008 NBA title, suffered a right ringfinger injury in the Lakers' Christmas Day triumph over the defending NBA champion Golden State Warriors and underwent surgery three days later.
Rondo has played only 14 games in an unlucky 13th NBA campaign, averaging 8.4 points, 6.7 assists and 4.4 rebounds after signing as a free agent last July.
He served a three-game fighting suspension and missed 17 games after breaking a bone in his right hand after undergoing surgery, playing only three games in five days before going out with his Christmas injury.
That was the same game where four-time NBA All-Star forward LeBron James suffered a groin strain that has seen him miss 12 games as well.
The Lakers ruled James out through Saturday's game at Houston but said he was cleared to return to practice next week, opening the door for a possible return for a rematch with the Warriors on Monday in Los Angeles.
"He seems to be in good spirits," Lakers coach Luke Walton said. "He's got another test tomorrow to get some more information on it. I think we'll get good news back."
If James misses the Rockets and Warriors games, the 14 consecutive game absence will be the longest such run of his 16-season NBA career.
James, 34, ranks sixth in NBA scoring with 27.3 points a game in addition to 8.3 rebounds and 7.1 assists for the Lakers, who at 25-21 own the eighth and final playoff spot in the Western Conference.