World No.1 Korda shot a three-under 69 second round to get to seven under at the Chevron Championship in Texas on Friday, leaving her one shot behind joint leaders Atthaya Thitikul (67) and Jin Hee Im (67) at the halfway point.
Steph Kyriacou was the leading Australian, five shots from the lead after a 69, while Gabriela Ruffels slipped to two under after a 73 to be one shot ahead of Sarah Kemp (73) while Robyn Choi (73) and Karis Davidson (74) scraped through the cut at two over.
Steph Kyriacou is well placed to make a weekend title challenge. (AP PHOTO)
But world No.5 Lee endured a dismal week, posting a 77 to miss the cut at seven over, along with fellow major winner Green (72, five over) and youngster Grace Kim (72, four over).
Kyriacou, 23, has two top 10 finishes in majors and believes she can step up this weekend.
"In the past I've kind of got scared of being in the spotlight," Kyriacou told LPGA Media.
"This weekend I'm going to embrace it a bit more and try to do what I did the last couple of days."
The 25-year-old Korda began the day two shots off the lead after opening with a 68 at Carlton Woods and made a double bogey at the opening hole but rallied with six birdies.
Korda is seeking her second major after winning the Women's PGA Championship in 2021.
She could join Nancy Lopez (1978) and Annika Sorenstam (2004-05) as the only players to win five consecutive LPGA events.
She was asked if it felt inevitable that she'd tie the record after her recent run of success and strong play in the first two rounds.
"I'm just at the halfway point right now. The amount of golf that I've played, I still have that to go," she said. "There is still a lot of golf left and anything can happen. Just going to stick to my process and vibe with ... what my coach says."
With increased attention on this tournament because of Korda's string of titles, what would the 25-year-old like people who might be seeing her first time this weekend to know about her?
"That I just never give up," she said. "No matter what, no matter how much adversity is thrown your way, they know that I never give up and I give it my all."
Thitikul, a 21-year-old from Thailand who has won twice on the LPGA Tour, missed the beginning of this season with a thumb injury. She made six birdies and one bogey on Friday.
Im is in her first season on the LPGA Tour after playing the Korean LPGA since 2018. She had a bogey-free 67.
Former world No.1 Lydia Ko, who won this tournament in 2016 at Mission Hills in the California desert, shot 71 and was part of a big group four shots back. She missed the cut last year in the Chevron's first season in Texas.
