The Reds narrowly missed out on the Premier League title last season as they finished two points behind winners Manchester City in second place.
Lawrenson feels that, if the club are to push on and win the title as well as compete in the latter stages of the Champions League next season, then their signings need to be spot on.
He wrote in his column in the Liverpool Echo: "If this season has been a test for Brendan Rodgers and his players, then the next few months will be all about the manager and his recruitment team.
"Having experienced a mixed transfer window last summer, the pressure will be on. And with Champions League qualification having raised the standard of prospective new signings, there is little margin for error."