Both sides clash at Upton Park on Saturday afternoon - the penultimate clash at the Boleyn Ground.
The Boleyn Ground plays host in a ground which will evoke strong emotions, given that it is the penultimate football match to take place at Upton Park, but the Hammers must put sentiment to one side and focus on reaching the Champions League next season.
Slaven Bilic's side sit sixth in the Premier League table, five points behind fourth-placed Manchester City with a game in hand - the visit of top-four rivals Manchester United on Tuesday for the stadium's curtain call - and a third straight win tomorrow would certainly boost their hopes.
The Irons have brushed aside Watford and West Brom in recent weeks, by an aggergate score of 6-1, and Lawrenson admits to being "really impressed" by the way in which the East Londoners have gone about their business in recent weeks.
Swansea City, however, may not be a pushover and they beat Liverpool 3-1 last weekend to illustrate that they will not roll over, despite not having much to play for, but Lawrenson says West Ham should have too much for them on the day.
"I have been really impressed by the Hammers of late and they are back in the race for fourth place, especially because they play Manchester United in their last game at the Boleyn Ground on Tuesday. 2-0," he told BBC Sport.