Bruce guided Villa to the Championship play-offs last season – only to miss out on promotion after losing to Fulham.
Lambert himself has managed Villa in the Premier League and he knows just how tough it will be for the new man at the helm.
“It’s difficult because of the expectation level really,” he told Sky Sports.
“The club was trying to get sold [when I was there] but the fans have got the history of a European Cup-winning football club.
“You’ve got that, a big fanbase behind you, who every time expect you to be up there.”
He may have had to deal with lofty ambitions from the Villa Park faithful but that didn’t stop Lambert loving life in the Midlands.
“I loved my time there – it was great, it really was a great club to be at and you move on for one reason or another,” he said.
“But the expectancy level was really really high, always.
“Dean Smith is going to have to master that side of it.”
Lambert spent three years at Villa before being sacked in 2015 with the club 18th in the Premier League table.
The Scot was replaced by Tim Sherwood but he was unable to stop Villa finishing rock bottom, 17 points off off 19th-placed Norwich.