Hadley made four birdies in the first six holes to open up a three-shot cushion at the turn but added only one birdie on the back nine for a five-under-par 67 at the Trump International course in Rio Grande.
"It was frustrating, to be honest," Hadley told reporters after signing for a 16-under 200 total with one round left.
New Zealander Lee (66) birdied the final three holes to jump into second place on 15-under, with Americans Jason Gore and Jonathan Byrd two shots behind.
Halfway leader James Driscoll plunged seven strokes behind after a 75 that did not include a single birdie.
Low scores were plentiful due to the soft conditions on a course that is fairly generous off the tee, which is why Hadley was not completely thrilled with his score.
"I hit it so well today (but) missed a lot of putts the last 11 holes," said the 26-year-old from North Carolina, who won twice on the secondary Web.com Tour last year.
He outlined an aggressive game plan for Sunday's final round: "You gotta stay aggressive out here. I'm going to go at just about every flag."
Lee seemed destined for stardom when, in 2008, he became the youngest ever U.S. Amateur champion at the age of 18, but his professional career has not quite taken off after a promising start.
"Everything is going really nicely at the moment," said Korean-born Lee. "I didn't even know I was in second place until the 17th hole.
"I didn't really want to know where I was at. I was just trying to be more focused on my round and not think about other stuff."
(Reporting by Andrew Both in Cary, North Carolina; editing by Julian Linden)