The Premier League returns this weekend after the international break but Aston Villa will have to wait till Monday to get back into action.
The Premier League newcomers have made a sluggish start to the season, having lost three of their opening four matches.
West Ham, on the other hand, bounced back from their opening day 5-0 defeat against Manchester City, to pick up two wins and a draw in their next three games.
In fact, the Hammers have won their last three games in all competitions.
Lawrenson says that he has seen ‘plenty of encouraging signs’ from Dean Smith’s side, and adds that they have signed some very good players during the summer transfer window.
He predicts it will be a close encounter, but Villa to narrowly edge their rivals at home.
“Aston Villa have only got three points to show from their first four games, but I have seen plenty of encouraging signs from Dean Smith’s side,” said Lawrenson to BBC Sport.
“They are still settling down, but I think he has bought some very talented players over the summer.
“West Ham are improving too, and are unbeaten since the opening day, with new signing Sebastien Haller getting among the goals.
“This one will be close, but I am going to go with Villa to make their home advantage count.”