The Blues will play host to Jurgen Klopp's team on Sunday.
The Reds' defence was 'all over the place' in the previous game, Lawro states.
Meanwhile, Chelsea had two good games against Liverpool last season and are getting only better.
"Chelsea kicked off their campaign with a good win over Brighton while Liverpool's performance against Leeds was a bit patchier, but with the same result," ex-Liverpool defender Mark Lawrenson told BBC.
"You wouldn't call it a mediocre display by the Reds, because their forwards got four goals, but it was the first time for a while that they weren't joined up from front to back. The defence was all over the place and yet the front three were excellent.
"It's nothing to worry about as a one-off, though, and in terms of joining things up Thiago Alcantara's arrival from Bayern Munich will strengthen their midfield. He is an upgrade on Georginio Wijnaldum, put it that way.
"Chelsea's attack will stretch Liverpool," Lawrenson added. "They gave the Reds some good games last season, and they have improved since then."
The 1-1 draw that Lawrenson eventually predicts might seem a bit generous given how difficult it was for the Blues to overcome Brighton on Monday.
Still, the Premier League champions are in the best shape either given the three goals they conceded from just-promoted Leeds United. Chelsea will have reasons to hope that Timo Werner & Co. could manage to exploit Liverpool's problems.
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