Lee, seeking her second title on the U.S. LPGA tour, had a 65 to stay atop the leaderboard at 13-under 129.
Thompson surged on the back nine with four birdies and an eagle on the par-4 14th at the Kuala Lumpur Golf and Country Club.
“It was right on line,” Thompson said of 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, who finished third in the recent Evian Championship, is chasing her second tour victory.
Last week’s Reignwood Classic champion, Feng Shanshan of China, also shot 65 and was third at 10 under.
Paul Creamer of the United States and IK Kim of South Korea were tied for fourth at 9 under.
Amy Yang of South Korea shot a tournament-record 62 to move into a tie for sixth, five shots 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.