The Aston Villa manager believes the Black Cats are still very much in the thick of the relegation battle ahead of the two sides' crucial encounter on Monday night
Paolo Di Canio has masterminded an upturn in the club's form since his arrival at the club to replace Martin O'Neill that has seen the Black Cats move six points clear of Wigan in the relegation zone.
But Lambert does not believe the north-east outfit have preserved their Premier League status yet.
"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," he told reporters.
"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 that was really good the way Everton have been playing but we're at home and the onus is on us to make the running."
Villa host the Black Cats on Monday evening in a proverbial six-pointer, but Lambert refuted suggestions there would be any ill feeling between himself and Di Canio on the touchline, despite the Italian - then in charge of Swindon Town - taunting Villa fans about relegation after a League Cup game earlier this season.
"I didn't know anything about it," he added. "I think I've got more things to worry about. I don't really get wound up by that sort of thing.
"The lads that go out and play, they're the most important people along with the people that come and watch it."