Lee had a steady 3-under-par 69 that moved him to 12-under 204 for the tournament as he seeks his first European Tour victory.
Mickelson had an eagle, two bogeys and nine birdies for a 9-under 63, was one off the course record, and jumped from a tie for 42nd to a tie for second.
Gaganjeet Bhullar, with a bogey-free 66 Saturday, is even with Mickelson at 10-under for the tournament.
Rory McIlroy was alone in second when play ended but was assessed a two-stroke penalty for an incorrect drop that left him with a double-bogey 7 at the second hole and a 2-under 70 for the round. He is tied with Pablo Larrazabal for fourth at 9-under 207.
Five players are tied for sixth at 8-under. That group includes second-round co-leader Rafa Cabrera-Bello, who was 1-over for the day after closing with back-to-back birdies.
Lee was 1-under at the turn after birdies a Nos. 6 and 7 and a ninth-hole bogey. He had birdies at 10 and 13 and fell back with a bogey at 16. A birdie at 17 gave him the lead going into Sunday.
Mickelson had four birdies and a bogey in the first six holes Saturday but really got everyone's attention with an eagle at the 597-yard, par-5 eighth. Just as on the front, he had four birdies and a bogey in the first six holes of the second nine. He then dropped a 30-foot putt for birdie at 18.