Playing on Friday afternoon at Seaview's Bay Course, Szokol followed her opening birdie run with a bogey on No.6, then added birdies on Nos. 8, 9, 13 and 16.
"Happy to get off to a great start and really looking forward to the weekend," Szokol said. "Lots of golf left. Really excited to see good golf and hard work paying off today."
The 30-year-old American teamed with Cheyenne Knight to win the 2023 Dow Great Lakes Bay Invitational for her only tour victory.
Top-ranked Nelly Korda opened with a 71, and No.2 Jeeno Thitikul had a 68. Maja Stark, the US Women's Open winner Sunday at Erin Hills, shot 70.
Lee birdied three straight holes three times - on Nos.3-5, 8-10 and 16-18 - and had one bogey in her morning round.
The 36-year-old South Korean won the 2013 Pure Silk-Bahamas LPGA Classic for her lone tour title.
"I don't have expectation," Lee said. "I just play golf. I just come out, have fun. That's all I do."
Japan's Akie Iwai was third after a 65 in one of only two 54-hole tournaments left on the LPGA Tour schedule. The other is the Walmart NW Arkansas Open.
"Normally four days, so I feel fast, shorter tournament," Iwai said. "That's why we must make a lot birdies."
Wei-Ling Hsu was at 66 with Aline Krauter, Ayaka Furue, Polly Mack, Saki Baba, Dewi Weber and Gurleen Kaur.
Robyn Choi is the leading Australian after shooting a three-under 68.
In a tie for 20th, Choi had six birdies but spoilt her card with a double bogey on the second that was followed by a bogey on the par-five third - her 11th and 12th holes.
One shot further behind in a tie for 34th is Karis Davidson, who had four birdies and two bogeys.
Defending champion Linnea Strom shot 72.
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