Weimann has progressed through the club's academy, having moved from Rapid Vienna as a 15-year-old.
Lambert said: "Andi has shown a great work ethic and that's the big thing about him, along with his quality.
"He has drive and a hunger to succeed and that's vital. That's what we're looking for here at Villa.
"He got a sustained run at it last season and he showed the quality that marks him out as a natural finisher. He definitely knows where the goal is and his performances on that right side, coming off the lines, have been really great.
"Whether Andi Weimann is on 'x' amount of money or not, you'll always get the same player - but we're delighted obviously that we've agreed this new deal."