Moyes has built on his good work at West Ham last season to put the Hammers right in the mix for a top four spot in the Premier League once again.
They hit choppy waters in recent games as they picked up just one point from nine available, but bounced back in style on Saturday as they defeated Chelsea 3-2 at the London Stadium.
There have been questions raised over whether West Ham can maintain their form over the course of a long season and Moyes appears to have hinted at similar concerns to Lawrenson.
Revealing a conversation with Moyes, Lawrenson said on LFC TV before West Ham beat Chelsea: “I spoke to Moyes [whose team are] in fourth place the other day and he said his team are just a little bit tired at the moment.
“I don’t think they have won for three games and they keep getting pegged back when they go in front.
“I think he’s just saying he hasn’t really got the squad at the moment.”
West Ham, sitting in fourth, boast a four-point lead over fifth placed Arsenal, who are next in action against Everton on Monday night.
Next up for West Ham is a return to European action in the Europa League, with Dinamo Zagreb due to visit the London Stadium.
