Inconsistency remains the enemy for the world No.5-ranked Australian, who on Friday hit an equal-low second-round 67 to move into contention.
But her chances fell away on Saturday, as she struggled to a 4-over 75 at the famed Baltusrol Golf Club.
Lee, winner of last year's US Open and the 2021 Evian Championship, carded four bogeys along with a double-bogey on the 13th as she slipped to a share of 26th, sending her into the final day one over.
Fellow Australians Grace Kim (69) and Gabriela Ruffels (68) retain an outside chance of snatching top spot from overnight leader Leona Maguire of Ireland.
Kim and Ruffels sit tied for 12th, six shots off the pace after 54 holes.
The in-form Maguire two-putted for birdie at the final hole to take sole possession of the overnight lead.
Maguire, who last week won the Meijer LPGA Classic in Michigan for her second Tour victory, posted a 2-under-par 69 to get to 7-under 206.
She is the only player in the field to have shot all three rounds in the 60s.
"I feel like I handled it pretty well and tried not to treat it any differently than any other round, just like last week," Maguire said.
"Same mindset (Sunday). One more day of patience."
South Korea's Jenny Shin, who made five birdies to charge up the leaderboard and reach six under late in the day, lies in outright second place.
Shin matched the low round of the week with her bogey-free 66. Her lone win on the LPGA Tour came in 2016, and she has had just two top-10 finishes at majors.
Stephanie Meadow of Northern Ireland shot a 67 to move into third at five under, while Lee-Anne Pace of South Africa (70) and China's Ruoning Yin (69) are tied for fourth at four under.
Rose Zhang, the 20-year-old prodigy who won her first professional start earlier this month, gave herself a three-foot eagle on the par-5 18th by hitting a 5-wood to reach the green in two.
She shot her best round of the week, a 68, and is tied with Kim and Ruffels for 12th at one under.
Steph Kyriacou (74) is in a share of 65th at seven over, while Hannah Green (75) sits a shot further back in joint 71st.
- with Reuters