The BBC pundit was not impressed with the way both sides crashed out of the Carabao Cup to League One sides on Wednesday and blamed the number of changes for those results.
Lawrenson has backed the Cherries to pick up all three points at the Vitality Stadium in a 2-1 victory, claiming their home advantage could play a big factor in the game against the Hammers.
Goals from Callum Wilson and Josh King secured all three points for Eddie Howe’s men in this fixture last season as they completed the double over West Ham.
“The Hammers have not won this fixture since the 2015-16 season, so how they do at Bournemouth will be a good indication of their progress,” he wrote on his BBC column.
“But Eddie Howe’s side are playing well and have got home advantage, so I am backing them to come out on top, just.”
After both sides were embarrassed in midweek, they will both be looking to bounce back in the best way possible – by securing three points in this Premier League clash. West Ham have their backs against the wall in this one though, having not beaten the Cherries in almost four years, as they crashed to two defeats against their weekend opponents last season. They also haven’t kept a clean sheet in that time, something the Hammers’ defence will be looking to rectify as they go into the game off the back of three consecutive shut outs in the league. Pellegrini will be quick to revert back to the side that comfortably cruised past Manchester United, and he will have faith that they can continue their unbeaten run at the same time. This is an early-season showdown between two clubs that want European football after their positive starts to the campaign, and the result after the game will send a message to teams in and around them at this time.