The Italian has been cryptic about his future at Brighton amid links to other clubs.
"We've seen how much money they've made this year," Lawrenson told Paddy Power.
I thought Roberto De Zerbi was a bit naughty last week, saying he wants more players. Brighton gave him his big gig, and he's done very, very well.
"But once you go down that route of asking for more players, and maybe his agent is speaking to other clubs, I don't think Liverpool will go anywhere near him.
"He's a good manager, but I think he is getting carried away Brighton haven't had a particularly good season. He's not dealt with the extra games and blamed it on not having enough players. De Zerbi won't go to Liverpool, and he might've put one or two prospective club owners off him.
"Brighton are a well-run club they got 22 million for Graham Potter and his backroom staff. They'll just get another manager in and being run the way that they are, they probably know who their next manager is."