Lyle completed 54 holes at 16-under-par 200. Back in February, he won for the first time on the Nationwide Tour at the Mexico Open.
Second-round leader D.J. Brigman managed a 2-under 70 in round three. He slipped into second place at 15-under-par 201.
Thomas Hagler IV, one of two amateurs to make the cut this week, fired a 9- under 63 to jump into a share of third place at minus-14. He was joined there by Doug Barron and Chris Kirk, who both shot 66 on Saturday.
Lyle started the round two behind Brigman. Both players birdied the first.
Brigman's two-stroke lead became four when he birdied the fourth and Lyle made bogey. Lyle fought back with birdies on the fifth and seventh at Fox Den Country Club.
'I got off to a good start,' Lyle stated. 'After the bogey at the fourth hole, I played just awesome. The way I'm playing I'm struggling to make bogeys, which is a good thing.'
The 32-year-old Brigman stumbled to a bogey on the seventh as his lead dropped to one shot. Two holes later, his lead was gone.
Brigman faltered to a bogey on the ninth, while Lyle made birdie to grab a one-shot cushion.
Lyle pushed his lead to three shots as he birdied the 10th and 11th. Brigman clawed back within one thanks to back-to-back birdies from the 12th.
The Australian Lyle traded a birdie for a bogey from the 15th. He parred the last two to get in at 16-under.
Brigman stumbled to a bogey on 17 to slide two back, but he atoned for that error with a birdie at the last.
'I was grazing edges all day long so it was a little frustrating,' Brigman said. 'I'm still in it. I don't know what tomorrow's going to bring, but at least I have a chance. The birdie on the last got me a little closer.'
Scott Parel fired a seven-under 65 to jump into a share of sixth at 12-under- par 204. He stands alongside Chris Smith (70), Arjun Atwal (68), Brad Fritsch (68), Keoke Cotner (66), Sebastian Fernandez (67) and Spencer Levin (68).