Indeed, the pundit feels the east London side will progress to the quarter-finals of the FA Cup at the expense of their Championship opponents.
And he believes West Ham are a 'decent side' even without their 'outstanding individual' Dimitri Payet.
Lawro told the BBC: "I think everyone has realised that West Ham are a very good team - now they just have to keep going.
"The Hammers also have an outstanding individual player in Dimitri Payet but, even when he is out, they are still a decent side.
"They have also come back late in a few games which shows they have resolve to go with that quality."
Lawrenson has become infamous for backing against the Hammers lately but doesn't want to make the same mistake here.
West Ham have a great chance to make a real impact in the FA Cup during their last ever season at Upton Park.
It all depends on their draw for the next round if they beat Blackburn, of course, while injury troubles are going against the east London side at the moment.
Blackburn fans will no doubt fancy their chances of causing an upset, however, with Paul Lambert wanting to prove himself against Premier League opposition after returning to management with Rovers, as well.