The Merseyside outfit will be looking to record successive Premier League victories to keep pace with defending champions Manchester City.
Liverpool FC started the new Premier League season with a 4-1 victory over Norwich City thanks to goals from Mohamed Salah, Virgil van Dijk and Sadio Mane.
The Reds followed up that result with a penalty shootout victory over Chelsea FC in the Uefa Super Cup in Istanbul after a 2-2 draw in 120 minutes.
Jurgen Klopp’s side will have two full days to recover before Liverpool FC make the long trip to the south coast to take on Southampton at St Mary’s.
Former Liverpool FC defender Lawrenson is confident the Reds can secure a straightforward victory over Southampton at St Mary’s.
“Liverpool do not have much of a turnaround between Wednesday’s Super Cup in Istanbul and Saturday’s trip to St Mary’s,” Lawrenson told BBC Sport.
“I still think the Reds will win on the south coast though.
“I did not expect Southampton to win at Burnley last weekend but I was amazed by how ordinary they looked.”
Lawrenson added: “Whether Saints just had a bad day – like Watford did against Brighton – I don’t know.
“That is not something that seems to happen to Liverpool very often any more and, even if they do, they still seem to be able to nick a win, or a draw at the very least.
“Jurgen Klopp’s side were criticised for their second-half performance against Norwich, but they were 4-0 up at the break in their first game of the season. No wonder they switched off a bit.”
Liverpool FC finished in second place in the Premier League table last season to narrowly miss out on a first title.
The Reds made amends for their Premier League disappointment with a 2-0 victory over Tottenham Hotspur in the Champions League final.
Liverpool FC have now won two major trophies under Klopp after their penalty shootout victory over Chelsea FC in the Uefa Super Cup final.
Klopp have signed Dutch centre-half Sepp van den Berg, Fulham teenager Harvey Elliott and West Ham goalkeeper Adrian.
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