Lee moved atop the leaderboard on Saturday (Sunday AEST) with another solid three-under round of 68, dotted with just the occasional starburst of brilliance.
It was enough to ensure he starts in the final group on Sunday alongside five-time major champion Koepka, who's scenting his first European tour title in 11 years.
The American moved ominously alongside the Perth star at 11 under with a brilliant 65, the best round of the day at the Golf de Saint-Nom-La-Breteche course.
Koepka, the LV Golf heavyweight, rattled off five straight birdies on the back nine to assume the role of favourite -- but Lee, shooting for his fourth European tour title, will take some beating as he seeks to find his best form.
"Just pretty solid again," shrugged the 27-year-old Lee, who's in his best form since winning his maiden PGA tour event in Houston in March.
"Didn't do anything spectacular in the back nine, but just hung in there. The shots were okay, and I'm just gonna go on the range and try to figure it out just a little bit."
For the second day running, Lee got off to a miserable start with a bogey at the first, this time after a three-putt, but he hit back by birdieing the third with an outrageous 37 footer.
He made another 18 footer at the fifth, before also birdieing the long sixth, and after firing to within seven feet of the pin for a birdie at 10, he produced his shot of the day at the par-four 13th, almost holing his approach from the semi-rough from 152 yards.
That put him into the lead for the first time alongside his English playing partner Marcus Armitage, who eventually slipped to a shot behind the leading pair after a 71. American Michael Kim and Italian Guido Migliozzi fired 66s to also move to 10 under.
The only blemish on Lee's card as he came down the stretch was a bogey at 15 after he had driven wildly out to the right behind the trees and ended with a bogey.
But the Australian is adamant his growing maturity can help him to another crown in what is the oldest national Open championship outside Britain in continental Europe.
"You've got to keep plodding along. The one thing I learned throughout my time as a professional, you've just got to keep hitting shots and keep mentally strong, but it's not done until the end, and you've just got to keep going, every shot matters," said Lee.
"If you're in the lead, you're doing something right, so you can just keep doing what you're doing."
Lee's fellow Australian Elvis Smylie is still right in the thick of the hunt too, just two off the lead in joint-sixth alongside local French hope Jeong weon Ko.
The left-hander's crowning moment on moving day was his 30 foot putt for eagle at the par-five sixth, which helped propel him to a four-under 67.
But the big danger to Lee looks to come from Koepka, who hasn't won since August last year on the LIV Golf circuit at the Greenbrier in West Virginia.
"I feel like my game has been trending in the right direction," he said.
