The Stadium of Light outfit have endured a poor season, and lie bottom of the table at the halfway stage of the campaign with just 14 points ahead of Villa's trip to the north east on New Year's Day.
Sunderland have improved in recent fixtures however, with three draws and a win in their last four outings.
And Lambert sympathises with opposite number Poyet after successfully staving off relegation himself last season.
"They are a club (that) not a lot of people would not have to be where they are," said Lambert.
"Gus has gone in there after another manager change and has tried to pick the club up.
"It's tough when you are down there, we were down there last season and you have to grind through it, but it is a big job."
Villa's best performances have generally come away from Villa Park this season, with the club losing just three times on their travels in the league.
The Midlands outfit will now look to repeat last season's 1-0 triumph at the Stadium of Light.
He added: "There is always pressure playing at home because of the fanbase but our away form has been pretty good, and we have had a few big players not playing for us.
"But our away form has been pretty good and there is less pressure there as you don't have the majority of the crowd on your side.
"We did well there last season and we will go and try and win there again."
