The 27-year-old birdied three of the last four holes for an eight-under par 64 on a steaming hot day to lead Ai Miyazato by one shot.
"I've waited so long, like seven, eight years," Lee said. "I really want to win this week. But two days more, two days left, so I'm going to try to keep being more confident and patient."
Temperatures climbed as the day progressed on Desert Ridge's cactus-lined Wildfire layout but Lee was able to complete her round before the heat kicked in.
"My driver was good," Lee said. "My tee shots keep in the fairway, and then my irons are pretty good, better than yesterday, and my putting works a little bit more."
Japan's Miyazato, who shot a tournament record 63 in the opening round, bogeyed the final hole to finish with a 67.
"I'm very happy with my round," Miyazato said. "I made eight birdies out there. I had three bogeys, but still a lot of birdies, so it just feels good. ... I kept hitting the fairways and I kept hitting to the green, and I had 29 putts, which is like my green regulation."
Stacy Lewis shot a 65 and was four strokes back in third, while defending champion Yani Tseng was two under after hitting a 72.
Michelle Wie again missed the cut along with Suzann Petterssen.