The Brazilian midfielder missed seven months of football with a cruciate knee ligament injury last season and saw his return cut short after he suffered a thigh muscle tear during an August clash with Manchester City.
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However, the 25-year-old is almost back to full training with the Reds and could now even be fit in time for the November 28 clash with Tottenham at White Hart Lane.
"Lucas has been out on the field in the last week or so which is great," he told the club's official website.
"He's not doing multi-directional movements yet but he's doing a lot of straight-line running and endurance work.
"I'm anticipating maybe another three weeks but his professionalism is great and he'll get back probably sooner than is anticipated."
Liverpool have endured a difficult start to the new Premier League campaign, having picked up just 10 points from their opening nine games.