Lee started her second round with a birdie on the first before going on to hit four consecutive pars.
She then let herself down with a bogey on the sixth before bouncing back with a birdie on the next hole.
The 20-year-old rookie remained consistent on the back nine as she hit three more birdies on the 12th, 15th and 16th to finish with a second round 67.
Two strokes behind Lee are Australia's Minjee Lee and France's Perrine Delacour.
Lee began her round with a bogey on the first, but rallied back to hit an eagle on the par-five third and a birdie on the fourth, seventh and 18th.
Delacour commenced her second round with a duo of pars before sinking a birdie on the third.
She followed that up with a hat-trick of pars and an eagle on the par-five seventh.
But, Delacour did not enjoy the same amount of success on her back nine as she hit a bogey on the 12th before finishing with a birdie on the 17th.
Three shots off the lead is South Korea's So Yeon Ryu, who hit a second round 69, which included three birdies and a bogey.
Klatten, who led after hitting a first round 65, faltered during the second round and plummeted down the leaderboard as she registered a 75, which consisted of a birdie, three bogeys and a double bogey on the par-four eighth.
World number one Lydia Ko finished tied 22nd and remains seven shots off the lead after a second round 69, which saw her hit four bogeys, including a hat-trick of them from the 15th to the 17th, and a bogey.
Inbee Park, who is ranked second, hit four birdies during her bogey-free round of 67, which was a major improvement from her first round 72.
Meanwhile, defending champion Lizette Salas was cut after she followed her first round 74 with a 73, which included two birdies and four bogeys.