The two sides head into this weekend's fixture on the back of Boxing Day defeats at the hands of Swansea City (1-0) and Hull City (3-1) respectively.
Lambert was pleased with his side's performance at the Liberty Stadium, while Gus Poyet was left ruing the number of Sunderland mistakes in their home defeat.
"History tells you that you've got to earn the right to stay in the league," he said. "Regardless of how big your name is or how big your club is, you have to earn the right to stay in the league.
"Everybody's the same. You take out that top six big clubs and everybody fights like anything to stay in the league.
"Sunderland, for some reason, have been down there as well for the last few years.
"They say you need 40 points. We've got 20 - last year I think it took us until January time to get that.
"So there's an improvement there, and we'll go and try to win on Sunday.
"We've found a way [of playing] that really suits us and there'll be so many twists and turns throughout this year. If we keep doing what we're doing, we'll be fine."
Having overturned Gabriel Agbonlahor's red card against Manchester United in time to face Swansea on Friday, Villa will be without the influential frontman due to an accumulation of yellow cards this weekend.
Former Sunderland man Kieran Richardson will also be unavailable, as he serves the last of a three-game suspension following his dismissal against West Brom.
Poyet, who has openly criticised the busy festive schedule, will be eager to avoid bookending the year with defeats to Villa, but concedes his side have defensive problems to overcome following their defeat to a Hull team who were previously winless in 10.
"We've got a few issues at the moment, problems at the back, and that's something we need to sort out," he said after the match.
Sunderland welcome back Connor Wickham following suspension, while Anthony Reveillere (calf) and Patrick van Aanholt (shoulder) remain sidelined.
