Lerner appointed Lambert last summer and is convinced the former Norwich boss can steer the midlands club through their current battle to avoid the drop.
He also has faith in the Scot to help Villa achieve their longer-term goals of stability and being a competitive force.
Lerner said: "In the time that I've come to know Paul, what is clear above all else is his strength of character and belief in his approach to football.
"Fortunes can shift quickly in this game and a sense that one has it right can become grave doubt in a matter of a few games.
"The Villa board knew that with Paul we would begin to address the club's multi-year lack of competitive stability by reshaping the squad with seven new signings in the summer.
"It has been rewarding at times this season although certainly frustrating as well, particularly recently.
"During January, Paul and the board have discussed a variety of players (to strengthen the squad) although nothing has yet materialised.
"I know also this can be frustrating as fresh players always give at least a sense of progress and optimism.
"Finally, and on a very personal note, I would reiterate that Paul has achieved success at many levels of professional football and I believe, given support, he will continue to do so for us."
Villa are 17th in the Premier League standings with 20 points, one point above the relegation zone and one below 16th-placed Newcastle.