Villa fell into the bottom three for the second time this season after Saturday's 1-0 home defeat by Southampton and have collected only one point from the last five games.
But weekend speculation that Lambert's job is under threat is regarded as "just total nonsense" by sources close to the midlands club.
Lerner and chief executive Paul Faulkner recognise the importance for stability and continuity at this juncture rather than another change of manager after the sacking of Alex McLeish last summer.
It is believed that Lambert's position has not even been an issue for discussion and Lerner recognises it is a long term project to rebuild Villa.
He also is mindful of the potential of Lambert who twice led Norwich to promotion and established them in the Barclays Premier League last season before moving to Villa in the summer.
The American is also willing to back Lambert during January although funds will be limited compared to some of the big spending carried