Lee, a winner at the Maekyung Open in South Korea in May, joined Koepka at the top of the Japan Golf Tour event leaderboard with a bogey-free performance.
They headed Angelo Que of the Philippines by one stroke, with world number four Hideki Matsuyama, the 2014 champion, among a group two behind.
Koepka and Matsuyama were able to stake their claim for the title by taking advantage of ideal conditions, with calm weather and receptive greens allowing for attacking golf.
Playing the back nine first, Matsuyama jump-started his round with a 30-foot eagle putt at the par-five 18th, where he read the green perfectly and curled a sharply-breaking putt into the middle of the cup.
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Koepka, two groups behind, responded by making four consecutive birdies around the turn.
Among other prominent players in the field, American Xander Schauffele, winner of the Tour Championship in Atlanta in September, carded a two-under 69, while Ryo Ishikawa battled to a 72.
Previous winners of the tournament include Tiger Woods, Ernie Els, Tom Watson and Seve Ballesteros.
(Reporting by Andrew Both in Tokyo; Editing by John O'Brien)
