The Uruguay international was drafted in from Benfica earlier this summer after Jurgen Klopp sanctioned a £64million deal for the powerful forward.
Nunez, 23, has arrived at Anfield off the back of a prolific season in Portugal - he bagged 34 goals in 41 games all told for Benfica.
And Lawrenson believes that there is no reason why Nunez cannot carry that momentum into the new campaign and put Liverpool on the front foot.
"I saw both the Liverpool fixtures against Benfica in the Champions League and, in all honesty, he tore us apart," said the former defender.
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