The former defender also believes the signing is a wise one as it adds some much needed experience to the side.
The England midfielder is the first signing of the summer for manager Brendan Rodgers, with him and his side expected to be busy as they look to strengthen their ranks after a disappointing campaign saw them finish outside the Champions League places.
And Lawrenson believes securing Milner will help attract other players to the club.
“Milner’s signing will also help attract other players to join,” he said.
“They’ll see him choose Liverpool above staying at City, and take that as a sign there must be positive vibes coming from Anfield. It’s still a place to be. Milner’s arrival [also] suggests Fenway Sports Group are relaxing their transfer policy slightly.”
The former defender also believes that, aside from helping attract other players, the signing of Milner is a good one for Liverpool in general.
More than anything, Rodgers’ side are losing a host of experience as both Steven Gerrard and Glen Johnson leave the club in the summer, although Kolo Toure has agreed a new deal. And Lawrenson believes the signing of the City midfielder will help to add much needed know-how to the side.
“There are many reasons why Milner makes sense,” he added.
“He is very experienced, and is versatile enough to play in several positions. Milner is the type of player we need, someone with experience, which is lacking in our squad now the likes of Steven Gerrard and Glen Johnson have departed.”