The Reds set up a Europa League quarter-final clash against Borussia Dortmund thanks to Thursday night’s 1-1 draw with Manchester United.
Philippe Coutinho cancelled out Anthony Martial’s opener from the penalty spot at Old Trafford after Liverpool were 2-0 winners at Anfield in the first leg.
Liverpool are unbeaten in their last four games in all competitions since losing to Manchester City in the League Cup final.
Former Reds defender Lawrenson believes Ronald Koeman’s Southampton side can bring Liverpool’s impressive run to a halt.
“Liverpool thrashed Southampton 6-1 at St Mary’s in the Capital One Cup in December, but I don’t see a repeat of that on Sunday,” Lawrenson told BBC Sport.
“It does not help Jurgen Klopp’s side that they played Manchester United at Old Trafford on Thursday, because that will take a lot out of them even though I expect them to win the tie.
“Southampton are inconsistent, but they got a really good win at Stoke last week, and it would not surprise me to see them produce a really strong finish to the season.”
The Reds are in eighth place in the Premier League table and seven points behind fourth-placed Manchester City, who occupy the final Champions League spot.
Liverpool were drawn against Borussia Dortmund in the Europa League quarter-final following their 3-1 aggregate win against United in their first meeting in Europe.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news