The Villa chief left Norwich to replace the axed Alex McLeish at the end of last season after taking the Canaries from League One to the Premier League in three successive seasons and then keeping them up.
And, having been tasked with the job of keeping outgoings down but improving results on the pitch, Lambert has struggled as Villa sit in the relegation places with just five wins from 27 Premier League games this season.
However, the Scot claims he was given a warning that it would not be an easy job to turn things round for the better.
"Randy Lerner said it would be tough from day one," BBC Sport quotes Lambert as saying. "I knew the parameters but it's a brilliant challenge for me to rectify."
Meanwhile, Lambert is hoping skipper Ron Vlaar will overcome a calf injury, which forced him out of last weekend's game at Arsenal, in time for Monday's visit of Manchester City.
Vlaar was unable to train during the earlier part of the week but the Dutch international defender was able to take some part yesterday and he will be assessed over the weekend.
Striker Darren Bent remains doubtful with a foot injury but keeper Shay Given has recovered from a groin problem in time to be part of the squad to face his former club.