The Galaxy have not yet replaced Beckham with another big-name, big-money player but they have been linked with England stalwart Lampard who looks likely to leave Chelsea when his contract expires at the end of the season.
"I am sure they have someone in the pipeline. I think it is important for the team to get big-name players in and if we get Frank it will be good - he's been on fire," Ireland striker Keane told Reuters.
Lampard, 34, has scored 10 goals in his last 15 games for club and country.
He netted in Chelsea's 4-1 victory over Wigan Athletic in the Premier League on Saturday and grabbed the winner in England's 2-1 friendly triumph over Brazil on Wednesday.
England manager Roy Hodgson said after the game that Lampard should stay in Europe to maintain his chances of playing in the 2014 World Cup.
The player has expressed a desire to prolong his 12-year stay at Chelsea.
An established international midfielder with an eye for goal is exactly the kind of player the Galaxy need, with their attempts to sign Brazilian Kaka from Real Madrid not having made any noticeable progress.
Keane said Beckham would be missed in the MLS after he joined Paris St Germain last month.
The 37-year-old former Manchester United and Real Madrid player spent six years with the Galaxy before he signed a five-month contract with PSG in January.
The transfer, however, prompted suggestions it was a marketing or business-led deal.
"It's not really hard to understand," said Keane. "It's very simple, he loves playing the game.
"Why would he not go to Paris? They are top of the league, they have a great manager (Carlo Ancelotti) who he knows very well after playing for him on loan with AC Milan. It makes sense regardless of all the other stuff.
"People are always going to question it because he is such a big figure but I know him personally and I know he just loves playing the game. What's wrong with that?" added Keane.
PSG have a six-point lead at the top of Ligue 1 and Beckham watched from the stands when they beat Valencia 2-1 in Spain on Tuesday night in the first leg of their Champions League last-16 tie.
Keane played alongside Beckham for two MLS seasons, winning the championship both times, and believes his former team mate can pick up another title this season.
"He still has passion for the game and he is still a quality player," said the Irishman. "He is going to a team that is probably going to win their league.
"It's not a bad place for him to be - hopefully he wins that league too because he has won in Spain, England and America. I hope he does it."