Lee, seeking her second title on the LPGA Tour, had a 65 that left her at 13-under 129. She led by four early on, but Thompson surged on the back nine with four birdies around an eagle on the par-4 14th.
"It was right on line," Thompson said, referring to the eagle. "But I couldn't see the bottom of the hole, but a few of the volunteers up by the green started yelling, so I was like, `All right, maybe it went in.'"
Thompson, third in the recent Evian Championship, is going after her second tour victory.
Last week's Reignwood Classic champion, Feng Shanshan of China, also shot a 65 and was at 10 under. I.K. Kim of South Korea (66) and Paula Creamer of the United States (67) were at 9 under.
Amy Yang of South Korea shot a tournament-record 62 at Kuala Lumpur Golf and Country Club and was among those five off the pace.
"It was a great round," Yang said. "I've shot 10 under before, but that was during a mini tour, so this is my best on the LPGA Tour and it feels great."
Defending champion and top-ranked Inbee Park shot par and was at 1 under.