The former defender also believes the increased competition for places in the squad is a good thing for next season.
The Spaniard joined the club from Sevilla last summer but endured an up and down campaign, which started brightly but faltered in the second half of the campaign.
He is the undisputed number one in the position though, with back up Jose Enrique hugely out of favour at Anfield and expected to leave should the club be able to sell him.
And Lawrenson says the club need a new recruit in that position to challenge Moreno given Enrique has clearly lost the faith of Brendan Rodgers.
“Liverpool need a new left back. You could ague [it] is the only position where the squad has an obvious weakness,” he wrote in the Liverpool Echo.
“Worryingly, [Moreno] quite often looked a little boy lost in the big games. [He] deserves another chance but we need more competition in his position, because it's clear Brendan Rodgers no longer has any real faith in Jose Enrique.”
Increased competition is good for the squad next season
The former defender also believes that manager wouldn’t want to be relying on summer recruit Joe Gomez as his main back up in the position given his young age.
Nonetheless, he is pleased with the work that has been undertaken in the transfer market so far this summer, with there now being increased competition in nearly every position.
The Reds have invested heavily this summer with a number of new faces arriving at Anfield and Lawrenson believes that is a good thing, as it is preferable to not have anyone in the squad not believing they are going to be playing every week.
“Joe Gomez can play in the role but, to be honest, you wouldn't want to be relying on someone so young and new so early in the campaign,” he added.
“Generally, though, nearly all of the people in other positions are under pressure for their place. You don't want anyone sitting in the dressing room believing they are going to be playing every week.”