The American made a superb start to the final major of the season at the picturesque resort above Lake Geneva, then managed to stay bogey-free.
Thompson, who was given an early morning start on the back nine in perfect weather conditions, was the sole leader for most of the day until Lee made up for two bogeys with seven birdies to tie for first place.
Thompson's run started when she birdied the 12th hole. Paired with Sandra Gal and former Evian champion Paula Creamer, she hit a 7-iron to 20 feet and sank an eagle putt on the 13th, and birdied Nos. 14 and 15.
Her day was capped by a remarkable bunker shot on her final hole.
''Ended up trying to go for the green, came up short in a bunker that was about 40 yards away, and chipped it short and had about 15-footer for par,'' she said.
The 20-year-old Thomson has won a major before, the Kraft Nabisco last year, but she went through a one-year drought before winning the Meijer Classic in July. She has three top-10 finishes in her last five starts.
Looking to complete a career Grand Slam, top-ranked Inbee Park could not find the accuracy that characterized her recent majors, and had to be content with an opening round of 1-over par. Park, who claimed the Women's British Open last month to become the seventh female to win four different majors, won the Evian in 2012, a year before the U.S. LPGA Tour made it the fifth and final major on its calendar.
Ko was the best of the elite trio, shooting a 2-under 69. She's bidding to become the youngest major champion this weekend.
Ko said she was impressed by Thompson.
''I saw her score. I kind of realized it was going pretty low, especially at the start of the round and she was only a couple of groups in front of us,'' she said. ''I was on the par-3, 14th or something, and that was only her fifth hole of the day. And I saw her to my left, and it showed her scorecard. I saw some birdies, some eagles, so that's a pretty consistent scorecard there.''
Michelle Wie's opening round was not as flamboyant as her aviator shades, new high-top pink shoes, and multicolored hair, as the 2014 U.S. Open winner headed into the clubhouse posting 75.
Although Wie and Paula Creamer (74) endured a bad day, Thompson's and Piller's bright openings were good news for the U.S. team for the Solheim Cup next week in St. Leon-Rot, Germany.