The Reds have invested heavily in their squad this summer, with Christian Benteke and Roberto Firmino big-money arrivals, while Nathanial Clyne, James Milner and Danny Ings have further supplemented their squad.
But Lawrenson feels Brendan Rodgers must still strengthen the left side of defence, with Moreno likely to start the campaign in the position, and with Jose Enrique likely to move on.
Speaking in his column for the Liverpool Echo, Lawrenson said: “There were some rumours knocking around last week that Barcelona were sniffing around Alberto Moreno.
“I’d be surprised if they want to take the Spaniard, given how, since the New Year, has been really, really struggling for form.
“Moreno started the season well after coming in from Sevilla and scored that fine goal at White Hart Lane, but it all fell apart in the second half of the season.
“Worryingly, quite often he has looked a little boy lost in the big games.”
Lawrenson added: “Moreno 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.
“Joe Gomez is a possibility for Liverpool at left-back
You could argue left-back is the only position where the squad has an obvious weakness in terms of strength in depth.
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.
“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.”
There’s been a few concerns expressed about Benteke’s fitness going into the new campaign, but Lawrenson feels the £32.5million signing must start in Sunday’s opener with Stoke.
“I’d be amazed if, should he stay fit, Benteke doesn’t start against Stoke City next weekend,” he added.
“If Brendan Rodgers doesn’t think Benteke is sharp enough, then how is he going to get that?
“By playing games. And, with the friendlies now all over bar the trip to Swindon Town, the only way the big striker is going to get that fitness, and build an understanding with his new team-mates, is by being out on the field.
“Benteke may well love playing against Stoke. It’s a chance for him to become an instant hero.
“And if you’ve paid that much for a forward, you may as well play him from the off.
“Imagine if Rodgers starts with Danny Ings or Divock Origi up front and Liverpool are losing 2-0 with Benteke on the bench. People will just wonder why Benteke didn’t start.
“It’s best to chuck him in and see how he goes.”