The Cottagers completed a league double over Liverpool last season and Brendan Rodgers' team have recorded just five wins out of 18 games at home in the whole of 2012.
The Brazil international hopes Liverpool can improve in the New Year in order to make Anfield the fortress it once was.
"It's important to make opponents fear coming to Anfield and make them know that it is going to be a tough afternoon for them," Lucas told the club's official website.
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"That's the way it was a few years ago and we need to get a good winning run going at Anfield again and make it more difficult for the other teams.
"We have had some difficult moments at home but we want to get the three points on Saturday and start a good run again."
The 25-year old went on to praise the quality of Fulham striker Dimitar Berbatov, who has been shining for his new side since his departure from Manchester United.
"We know Berbatov is a top player," he added. "He has a lot of quality and he is very dangerous so we need to be careful of that.
"He does like to drop deep so sometimes I will be around him and try to stop him being available for a pass and try to stop him creating chances for his teammates."