West Ham will take on Sunderland at the Boleyn Ground in the Premier League on Saturday afternoon.
Former Liverpool defender Lawrenson has predicted the Hammers to pick up all three points from the encounter courtesy of a 2-1 victory.
The former Republic of Ireland has also urged the West Ham fans not to boo Sunderland manager Sam Allardyce.
“There is talk Allardyce might get a mixed reception from the home supporters on Saturday but, as a West Ham fan, why would you boo him?” Lawrenson told BBC Sport.
“He kept your team in the Premier League and made some good signings who are still there. Now they have improved and are playing really well, but he has played his part in that too.”
Allardyce was in charge of West Ham for four years from 2011 until the end of the 2014-15 season.
The Englishman did a good job at the Boleyn Ground, keeping the Hammers in the English top flight and establishing them as a Premier League side.
The main criticism levelled at Allardyce was that his football was not pretty, and while that might be fair, the good work he did for the London outfit cannot be denied.
West Ham are seventh in the Premier League table at the moment, while Sunderland are second from bottom in the standings.