Pulis has performed a minor miracle since taking over the helm at Crystal Palace towards the end of November, when the club were rock bottom with just seven points from 12 matches.
Pulis has since steered the Eagles out of the relegation zone to a position where they are now seven points clear of the bottom three ahead of Saturday's game against a Villa side one place above them.
The last two games have seen Palace spring a shock success over Chelsea and then comfortably beat relegation rivals Cardiff 3-0 in south Wales.
Although Palace are not mathematically safe yet, Lambert said: "It wouldn't surprise me if Tony picked up something.
"He did brilliantly when he was at Stoke, and he's doing really well now at Palace.
"I get on pretty well with him, and you know what you get with Tony's sides, that it's going to be a hard game.
"He's a squad of good, honest pros who have picked up a couple of good results lately that has given them a fighting chance."
Whereas Palace have clawed their way back up the table with the two recent wins, Villa have slipped back into the dogfight after a run of three straight defeats that followed their own surprise victory over Chelsea.
Given the gap to the bottom three both Villa and Palace would appear to be safe - and they are odds of 12/1 (Villa) and 25/1 (Palace) to be relegated - but Lambert knows nothing can be taken for granted.
"Nobody has ever indicated we are safe," added Lambert.
"You just try to get over that line as quick as you can, and you have to win games to do that, and we know we're capable of winning games.
"I'm also confident we can do that. You go into every game thinking you can win it."
Asked about Villa's minimum requirement from their last six matches, Lambert replied: "Just to get as many wins as we can.
"But I don't think it will take 40 points, not with the way the table is. I don't think that will happen.
"We just have to get wins, just like everybody else and as quick as we can."
Lambert at least has a trio of key players available again for the game after fielding a depleted side for last Saturday's 2-1 home loss to Fuhlham.
Striker Gabby Agbonlahor and midfielders Fabian Delph and Karim El Ahmadi should all go straight back into the starting line-up.
Villa are still reeling, though, from the blow of losing star striker Christian Benteke for at least the next six months after he ruptured an Achilles tendon in training last week.
With Libor Kozak and Nicklas Helenius also sidelined, that has thrown January transfer window capture Grant Holt firmly into the fray.
Holt, who previously worked with Lambert at Norwich, responded with the equaliser against Fulham, but was unable to prevent Villa from sliding to a disappointing loss.
Lambert at least knows he can rely on Holt given the battle Villa find themselves in as he said: "I thought Holty was great on Saturday, he really was.
"It was his first full game since October and I thought he led the line fantastically well for us and he scored a really good goal.
"The thing with Grant is he has been over the course before and he knows exactly what it's like, he's been in every league going, been around the block.
"So I've no fears about him being able to do a job for us."