The Scot's first game in charge was the encouraging 0-0 draw at Preston. But the Championship side have still not won in eight games, their worst run since the 2012-13 relegation season.
"One of the biggest differences is the work rate," said Bodvarsson.
"We're playing much faster and defending better," he told BBC WM.
"The message is much more clear now. A lot of the guys are taking it very positively.
"Paul Lambert has obviously come in with a plan. It is a clear message to all of the guys in the team about what their job is on the field now.
"Defensively, we were very good at Preston. Other than needing to be a little more clinical in the final third, I think we're improving a lot."
Iceland international Bodvarsson was one of previous boss Walter Zenga's first summer signings when he joined from German second-tier side Kaiserslautern.
Lambert's first home game in charge of 19th-placed Wolves is on Saturday against ninth-placed Sheffield Wednesday.
Wednesday have lost on their last five visits to Molineux, in a run of just two wins in 26 matches against Wolves.
Wolves' all-time leading scorer Steve Bull and fellow club legend Andy Thompson will make on-field appearances to mark the 30th anniversary of their moves to Wolves from neighbours West Bromwich Albion.
The club are expecting an attendance figure of 28,000, close to Molineux's 31,700 capacity, and comfortably their biggest crowd of the season.
Wolves striker Jon Dadi Bodvarsson says they are already getting a much clearer "message" of how to improve under new boss Paul Lambert.