The Hammers will take on Palace at the Boleyn Ground in the London derby and will be looking to return to winning ways.
Sam Allardyce’s side have not been in great form in recent weeks and have been able to win only one of their last nine league games, taking eight points from a possible 27.
Palace are struggling for survival in the Premier League, although the Eagles’ results have improved under manager Alan Pardew.
The London outfit are sixth in the league form table based on the last six games, although they have not won any of their last three competitive matches.
West Ham will be favourites to win against Palace, especially as they are at home and had a good game against Tottenham Hotspur at White Hart Lane last weekend.
Lawrenson has backed the Hammers to pick up all three points on Saturday and wrote on BBC Sport: “West Ham played well in their 2-2 draw with Tottenham but the problem was they did not win a game that they really should have done.
“To be denied three points by somebody following up a 96th-minute penalty is painful. Pardew would love to do something similar against his former club but I don't see West Ham slipping up this time.”
West Ham are currently eighth in the Premier League table with 39 points from 26 matches, eight points behind fourth-placed Manchester United.
Meanwhile, Palace are 13th in the standings with 27 points from 26 games, just five points above the relegation zone.