The Black Cats have furthered their hopes of survival with two wins in the three games since Paolo Di Canio took charge at the Stadium of Light.
The two teams meet at Villa Park on Monday night and Lambert said that it will be up to his team to force the issue.
"A lot can be made of a new manager coming in and it's up to us to combat that and go and try to win," Sky Sports News quotes Lambert as saying.
"You don't know if it's worked, you have to wait and see, they're still bang in it. I think Paolo would say that himself.
"You can talk about new manager syndrome or whatever but it's the same group of players that were there before. They got a result against Everton but we're at home and the onus is on us to make the running."
Villa are three points above the drop zone.