Lee, who won her third major at last month's US PGA Championship, is in a large group sharing third place that includes American world No.1 Nelly Korda after Thursday's round at Dundonald Links.
Five players are in a share of second with Ireland's Leona Maguire, Japan's Rio Takeda, Spain's Nuria Iturrioz, England's Lottie Woad and Thailand's Arpichaya Yubol all on five-under-par.
England's Charlotte Laffar, who carded eight birdies and two bogeys in getting to a six-under 66, holds the outright lead.
Laffar, 32, only returned to the Ladies European Tour in May after taking four years off to have two children.
"I've got no pressure at all," Laffar said.
"Golf is a lot of people's lives out here, but my children are my life.
"So this has become more of a working hobby, I suppose you could say.
"I have just got to enjoy every moment, I don't know how long I'm going to do it for ... I've got to show the kids how I used to play."
Former world No.1 amateur Woad, had held top spot on her own after six birdies in 14 holes, including almost holing her tee shot at the short 11th.
But the 21-year-old's only bogey of the day at the par-four 17th dropped her back into the group sharing second, which includes Ireland's Maguire - herself a former No.1 -ranked amateur, after signing for a 67.
Perth star Lee is making her ninth assault on the Women's Scottish Open with the world No.5 never having finished worse than tied 18th in the event.
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