Pulis was named Palace manager in November when the club were bottom of the Premier League, but he has managed to guide them to 14th ahead of their match against Villa on Saturday afternoon.
"I'm not surprised by the turnaround he's made there," Lambert told reporters.
"I don't think he would have taken it on if he didn't think he had a chance of doing it.
"They weren't too detached from anyone. Yeah, there was a lot of work to be done but I never thought for one minute Tony couldn't get them clear of danger."
Palace can go above Villa in the table with a victory on Saturday.