The Hammers have had an impressive start to the season, as last weekend's win away at Manchester City now means that Slaven Bilic has won four of his six Premier League games - including away wins at Arsenal and Liverpool.
Two home defeats mean that some fans and pundits have wondered whether Bilic's side are better suited to playing away from home - and now they have a chance to prove that wrong when they face Norwich City this weekend.
The Canaries claimed a surprise draw away at Liverpool last weekend, and Alex Neil's side also beat West Bromwich Albion 3-0 in the Capital One Cup in midweek.
Now, they are looking to join Bournemouth and Leicester City in being the only teams to beat West Ham in the Premier League this season - but Lawrenson believes it will be a draw.
Speaking to BBC Sport, Lawrenson has predicted a 1-1 draw between the two sides, and believes that Bilic faces two big problems - the lack of ability to counter attack at home and the notion that West Ham have now become a scalp having beaten some of the biggest clubs in the country this season.
"Norwich got a really good point at Anfield last weekend although I felt they only played well until they got into the final third," said Lawrenson. "The Canaries only really made two opportunities, scoring from one and then forcing Simon Mignolet into a great save with the other."
"West Ham have had three fantastic away performances - against Arsenal, Liverpool and Manchester City - that they could only have dreamt of. But I think it will be harder for them at home, firstly because Norwich will not come forward in numbers to allow the Hammers to counter-attack, and also because Slaven Bilic's side are now a real scalp," he added.