The Saints will head into the Premier League clash at St. Mary’s Stadium on the back of a 1-0 victory over Queens Park Rangers at Loftus Road.
Meanwhile, West Ham conceded a late goal against Manchester United at the Boleyn Ground on Sunday to draw the league encounter 1-1.
Lawrenson believes that Ronald Koeman’s Southampton will build on the win against QPR and pick up all three points against the Hammers at home.
“Southampton were not great against QPR at the weekend but they still won,” the 57-year-old wrote on BBC Sport.
“They have key players like Morgan Schneiderlin and Victor Wanyama coming back to full fitness too, and it will make a big difference when they get the heartbeat of their team back.
“I think they will beat West Ham too. The Hammers played really well in their draw against Manchester United on Sunday, but I think it will have taken a lot out of them. They looked very leggy at the end.
“West Ham need to have some of their injured players back soon too, especially at the back. Cheikhou Kouyate scored against United and played well, but he is going to give up chances.”
Southampton will indeed be favourites to win against West Ham, especially as they are at home and are gunning for a top-four finish in the Premier League this season.
The Saints have conceded just eight goals in 12 league games at home, while the Hammers have scored 16 in 11 away matches.
The game at St. Mary’s will be tight and competitive, and one suspects that a single goal could decide the outcome.