The Reds were impressive 3-2 winners against Ligue 1 giants Paris Saint-Germain in their opening Champions League fixture on Merseyside mid-week.
Roberto Firmino came off the bench to score a winner deep in added time after Daniel Sturridge and James Milner netted in the first half at Anfield.
Liverpool FC have a 100 per cent record in the Premier League this season to keep pace with current leaders Chelsea FC.
The Reds have beaten West Ham United, Brighton, Crystal Palace, Leicester City and Tottenham Hotspur in the current campaign.
Southampton have only managed to record one victory in their opening five games to leave Mark Hughes’ side in 13th place in the table.
Former Liverpool FC defender Lawrenson believes the Reds will ease to a 3-0 victory over Southampton in their sixth fixture of the season.
“After having Neymar and Kylian Mbappe in town in midweek, this game might not have the same glamour about it for Liverpool, but it is still one they need to win and Jurgen Klopp will not accept any drop in effort,” Lawrenson told BBC Sport.
“The Reds are on a real high at the moment and I think they will make it six wins out of six in the Premier League.”
Liverpool FC finished in fourth place in the Premier League table last term to ensure their continued participation in the Champions League.
The Reds signed Fabinho, Alisson Becker, Naby Keita and Xherdan Shaqiri in the 2018 summer transfer window to boost Jurgen Klopp’s squad.
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