Somerset opener Trescothick, who played in 76 Tests for England, said: "I was gobsmacked. You don't normally see these things go on so close to a series, so for that to happen was a big surprise."
He added: "We play Australia this week at Taunton. I'll be very interested to see how they go about things.
"It's going to go one of two ways. Either they'll really rally around Darren Lehmann - he's a good guy, very well liked in the Australia set-up and a good coach.
"Or, if England can get on top and put them under pressure in the first game, or first couple of games, you might see a few cracks exposed."
But paceman Shaun Tait thinks Australia's hopes for the series have improved since Lehmann's appointment.
"In my opinion he's the man for the job," Tait said. "My mind's changed a bit since the appointment of Lehmann. Two days ago it was very difficult to see Australia win the series, but I've changed my mind slightly.
"They've got more of a chance than people might think. The Australian cricket team probably needed something, needed a little bit of a kick-start.
"People say it might be a surprising time to do it, but it's probably not a bad time."