Lambert was in charge of Villa from 2012 until 2015, while Smith has just been appointed as the new manager of the Villans following the departure of Steve Bruce.
Smith has joined Villa after leaving Championship rivals Brentford and is a fan of the Villa Park outfit.
The Express quotes Lambert as saying: "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.
“But the expectancy level was really really high, always. Dean Smith is going to have to master that side of it.”
Pushing for promotion
Villa are a big club in England, and the expectation are indeed high - as they should be.
The Villans should be in the Premier League, and Smith has been entrusted with the task of leading the club back into the top flight of English football.
Although Villa’s results and performances so far this season have not been great, they are still very much in the running for the Championship playoffs.
A few good results, and Villa will be up there in the top six, and after that, anything is possible, as the Championship can change very quickly.
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