The New Zealander climbed into outright second after posting eight birdies and two bogeys at Bethpage Black in New York on Thursday.
Lee, whose best major finish was a tie for 17th at the 2016 Masters, capitalised on the par-threes, birdieing three of the four shorter holes.
The 28-year-old said he was able to take his chances to sit a shot behind defending champion Brooks Koepka.
“I can’t remember every single shot I hit, but the only thing I can remember is whenever I hit it on the fairway, I was able to convert that to the birdie,” Lee told a news conference.
“I think I made a lot of good up-and-downs, I think, even when I missed the fairway.”
On his success at the par-threes, Lee said: “My iron game has been always good, and I always have a lot of confidence in them.
“And I guess I really liked the pin locations, what they gave us, and I was able to go straight at it every single time.”
While Lee was impressive, the day belonged to Koepka as the American set a new course record with his seven-under 63.
But the three-time major champion’s round came as no shock to Lee.
“I wasn’t surprised when Brooks shot seven under this morning. I mean, have you seen him playing U.S. Opens and PGA Championships the last three years?” he said.
“When you’re hitting driver, pitching wedge every hole. I wasn’t surprised at all. But it didn’t change my game plan at all.
“I’m not like Brooks Koepka long, but I can carry it about 290, 300 now. My mindset was honestly some kind of under-par round would be good, but obviously I did a lot better than that and I was very pleased with it.”
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