On a day when the average score soared as high as the mercury to almost 77, Lee carved out an even-par second round of 72 to stay strong at three under for the championship.
The one-time world No.2 trails Thailand's now-world No.2 Jeeno Thitikul by three shots entering the weekend climax after the superstar Thai shot to six under with a late flurry.
Chasing a maiden major, Thitikul birdied her last two holes in a second-round two-under 70 at PGA Frisco's Fields Ranch East course.
The 22-year-old one-time world No.1 will carry the 36-hole lead into a major for only the second time, having tied for 12th after being the halfway pacesetter at the 2024 Chevron Championship.
"I feel really good," Thitikul said.
"To be honest, I just said to my coach if anybody can shoot under par today, that player will be really, really great - and I'm shooting two under."
Playing as close to a home game as the Perth-raised, Dallas-based Lee gets, the Australian offset three early bogeys with three birdies to stay firmly in the mix for a third major title of her own.
Significantly, unlike the first round when she dropped two shots in the last three holes, Lee hung tough down the stretch with three back-nine birdies after slipping four strokes behind at one stage.
"I started a little bit shaky. Turned in two over but I knew there were a few opportunities on the (back) nine to make a couple birdies," she said.
"I just tried to stay patient out there. It was really windy and quite hard to even hold the greens on some of them.
"So I just tried to stay within myself and just be smart and play to my advantages."
Her late rally left Lee level with Japan's Rio Takeda, who carded a one-under 71 to be tied for second.
The pair are one shot ahead of sentimental favourite Lexi Thompson.
The American continues to revel since retiring from fulltime professional golf, Thompson climbing to fourth with a two-under round on Friday morning (Saturday AEST).
Japan's Chisato Iwai and American Auston Kim, who both posted second-round 72s, are the only other players in red numbers at one under par.
World No.1 Nelly Korda (74) is tied for 16th at two over after managing only one birdie for the day.
Steph Kyriacou (75) is the next best of the Australians, one shot behind Korda, at three over and equal 25th.
World No.8 Hannah Green is another stroke back after producing the shot of the day, a hole-out eagle at the par-5 13th, in a rollercoaster round of 74 that also featured a double bogey, four bogeys, two birdies and 10 pars.
At five over after a 74-75 start, Karis Davidson also earned a weekend tee time after taking a sabbatical from golf last year to complete an aged and disability care course on the Gold Coast.
At seven over, fellow Australians Gabriela Ruffels (77-74), Hira Naveed (75-76) and Grace Kim (73-78) all survived the cut by a shot.
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