Lawrenson believes the player would felt more than four times that sum now.
"What was it - £8.5m [initial £8m] or something [they paid for him]? He is probably times that by five at the moment," Lawrenson said to BBC Scotland.
"I cannot remember a poor game from him.
"People in the game said to me, 'He is great going forward, but defensively against the top teams, I am not sure.' I tell you what, no-one has taken him apart as yet.
"The quality of his passing and crossing is outstanding. He is an extremely fit individual; he just looks like a player that doesn't give a problem to the manager and gets on with it.
"He has got all the tools. We will probably have a better indication at the end of next season. I always judge a player over two years," the five-time First Division winner admitted.
"Sometimes they come in and have a great first season, and the second season is maybe not quite as good. That is when you really decide if they are going to be a great, or just a very, very good player. But very, very good at Liverpool is totally acceptable."