The Reds host the Hammers on Merseyside fresh from reaching the League Cup final thanks to a 6-5 penalty shootout victory over Stoke City at Anfield on Tuesday night.
Reaching the Capital One Cup final will lift everybody in Jurgen Klopp’s squad, and bring extra competition for places
Liverpool have already lost twice to Slaven Bilic’s Hammers side so far this season after a 2-0 loss at Anfield in August was followed by a 3-0 defeat at Upton Park in January.
Writing in his BBC Sport column, former Liverpool defender Lawrenson backed Jurgen Klopp’s side to end their miserable run against the Hammers on Saturday evening.
“I am at Anfield for this game and expecting to hear a few songs from the travelling West Ham supporters who have been unhappy with my predictions – I will give them a wave,” Lawrenson told BBC Sport.
“The Hammers have beaten Liverpool twice this season in the Premier League with an aggregate score of 5-0, so they definitely know how to play against them.
“The question is, will Liverpool have learned from what happened in those games? I don’t think they will be as bad as they were at Upton Park earlier this month.
“I also think reaching the Capital One Cup final will lift everybody in Jurgen Klopp’s squad, and bring extra competition for places.
“So I am going to go for a Liverpool win, which will really please my new West Ham friends.”
Liverpool haven’t won the FA Cup since 2006 when Steven Gerrard scored twice to force extra-time at Millennium Stadium.
The Reds won their only FA Cup crown under Rafael Benitez thanks to Liverpool’s penalty shootout win against the east London side.
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news