The Hammers opened their Premier League campaign with a 2-1 defeat away at Chelsea, as Diego Costa's late goal condemned Slaven Bilic's men to an agonising defeat.
Today is a historic moment for West Ham though, as they play their first Premier League game at the London Stadium having moved from Upton Park this summer.
West Ham players training at the London Stadium
Fans will want to start their new era with a win, but they will also be wary of how they were beaten by Bournemouth at home last season.
The Cherries had just won promotion to the top flight and picked up a stunning 4-3 win at Upton Park, with Callum Wilson bagging a hat-trick.
Eddie Howe's men kicked off this season with a 3-1 home defeat to Manchester United, and will be hoping to spoilt West Ham's party at the London Stadium this afternoon.
Bournemouth's Eddie Howe applauds fans
Lawrenson is in fact backing West Ham to win today, but thinks Bournemouth could pose a real test for the Hammers, who will be wary of many other clubs initially struggling upon moving to a new stadium.
The former Liverpool defender also thinks West Ham's task has been made harder by the injury to new signing Andre Ayew, who could miss four months having suffered a thigh injury against Chelsea.
West Ham United's Andre Ayew receives medical attention before going off injured
"Bournemouth aren't great defensively and they know it, which is why they took Marc Wilson from Stoke this week," said Lawrenson. "Eddie Howe's side are so open teams will always create chances against them but I don't think it will be easy for West Ham."
"Their late defeat at Chelsea on Monday, then the news that Andre Ayew has been ruled out for four months, has turned this into a difficult game for the Hammers. Their first league game at the Olympic Stadium is a big occasion but it might be Bournemouth who supply the euphoria."
"The Cherries edged an absolute thriller 4-3 in this fixture last season and I am tempted to back them to get a point - but I am going to go with West Ham. If that happens, it would be two defeats out of two for Bournemouth. They only won one of their last eight games last season too, and they have to be careful that their poor form does not continue too much longer," he added.
What's your prediction for West Ham United v Bournemouth?