The German has been a big hit at Anfield since arriving as Brendan Rodgers’ replacement back in October.
He enjoyed one of his best games in charge on Thursday evening as he guided his side to a scintillating 4-3 victory over former club Borussia Dortmund.
It was a win that echoed some of the great European nights at Anfield as they sealed their place in the Europa League semi finals.
Lawrenson was particularly impressed by how Klopp saw his side to the win, saying there are echoes of Reds legend Shankly about their current boss.
"When Jurgen Klopp was appointed everyone in England thought it was a great job,” he told BBC Sport.
“There are touches of Shankly in there. He's a really, really good fit and he has raised this average team."
The future certainly looks bright under Klopp at present, with this display the latest in several big performances under him.
Much is likely to rest on the work he can do in the summer transfer window, with many eagerly anticipating a big season for the side next season.
And another who was impressed was former Manchester United midfielder Owen Hargreaves, who says signing a couple of players could see Liverpool going places.
“Tonight was another where everything he touches turns special,” he told BT Sport.
“I just think he’s one of those managers that motivates the players. He is building something very special here; add a couple of players in the summer and Liverpool are going places.”