The Hammers are unbeaten since their opening day defeat to Manchester City, and come up against a Villa side who have won just once and currently reside in the bottom three.
But speaking to BBC Sport, Lawrenson believes that the Villans can upset the form book.
He said: “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. 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.”
Lawrenson has predicted a 2-1 win for Villa.
This one could go either way, to be fair, but you would hope that West Ham have enough to see this one through. The Villans are due a win, but the Hammers look sharp at the moment, and that 2-0 win over Norwich City, following on from a 3-1 win over Watford, looked about as assured as they have for quite some time under Manuel Pellegrini. Sebastien Haller has been picking up the plaudits, and rightly so, but it is no coincidence that the Irons have started winning ever since Mark Noble came back into the side. The skipper has averaged three tackles per match since returning from injury, as per Whoscored, as well as one key pass and a pass completion rate in excess of 87%. He is the perfect partner for Declan Rice in that engine room, and his presence has made a huge difference to West Ham’s fortunes in recent weeks. With him in the lineup, don’t be surprised to see them win again.