Lee birdied the first six holes, and had 11 birdies overall, to equal the lowest round in a European Tour event this year. The 348th-ranked Lee was 16-under 197.
Thomas Bjorn, the 2011 champion from Denmark, Alejandro Canizares of Spain and Victor Dubuisson of France were tied for second.
Lee, who has never won a European Tour event, said it was "comfortably my best round ever."
"It was surreal to see all these great golf shots go down on the same day," said the Scot, who birdied nine of the first 10 holes and briefly threatened to shoot the first 59 on the European circuit.
Miguel Angel Jimenez of Spain, the 2010 champion, and Tommy Fleetwood of England both shot 69 to sit five shots behind Lee in a tie for fifth place.
On another day of low scoring in the Swiss Alps' thin air and sunshine, Ross Fisher of England shot 63 to be 10 under, six behind Lee. Fisher was joined by American Brooks Koepka, who went round in 69.
Lee covered the outward nine in 28 strokes, equaling the best this year on the European Tour, by Chinnarat Phadungsil of India at the Avantha Masters in New Delhi.
Only Phadungsil and Tiger Woods, at the Bridgestone Invitational -- an event co-sanctioned by the European Tour -- shot 61 this year before Lee matched them.
"It was pretty special. You get off to a start like that and it steadies the nerves," said Lee, whose card was blemished by a bogey at the par-14 12th after he pushed his tee shot into trees on the right.
He came straight back with two more birdies, including an 8-footer on the par-3 13th to bring the elusive 59 into sight.
"The 59 crept into my head coming up the second par 5, at the 15th," said Lee, who parred the last four holes.
Asked how he would prepare for the last day's play as leader, Lee joked: "I don't know. I've never done it before."
Lee was playing with an injured left hip which he said was heavily taped, and revealed he was more concerned recently with retaining his tour status for next season.
"It's pretty tough to change your mindset overnight," said Lee, who is 108th on the European money list.
Richard Finch of England made a hole-in-one at the 208-yard 13th.