Lancaster took over as interim coach in March 2012 after Martin Johnson stood down from his role as England boss following a disastrous World Cup campaign blighted by off-field controversies.
The 42-year-old led England to four victories in their Six Nations campaign earlier this year, with the Red Rose only losing to eventual Grand Slam champions Wales.
Baxter, who will oversee Exeter’s first campaign in the Heineken Cup this season, is confident Lancaster is making great strides in fostering a “club spirit” in the England camp, which the Chiefs boss says is crucial to the success of the national team.
“I know Stuart very well. He’s a decent, straight talking person,” said Baxter.
“It’s very important to him that England play well and they show that it’s important they are playing for their country.
“There’s a genuine passion that England comes first and the things that come with representing the national team are bonuses – and not the other way round.
“I think he’s keen to establish that.”
Baxter added: “He wants the players to be proud to play for their country, proud of the players around them and the way they want to be seen as playing.
“For me, that’s always a good starting point. If you can establish that, almost a club spirit within an international team, you’ve got a really good foundation.
“I think that’s what Stuart’s real ambition is to get that established first. He’ll build from there then.
“I’m not massively worried about the style England are playing, that will come over a period of time, once we’re really confident that the players are pride to play for their country.”
Exeter Chiefs are fuelled by www.myprotein.com, the UK’s number one online sports nutrition brand and supplier to many of Britain’s elite athletes including Olympic Bronze Medallist Gymnast Sam Oldham, world 400m hurdles champion Dai Greene and 11-time Paralympic gold medallist David Roberts.
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BIOGRAPHY: Anthony Martial