Lee, starting at four under, dropped a shot on his first hole but fired back with four birdies in his next five chances at Memorial Park Golf Course on Friday (Saturday AEDT).
He nailed his approach to the par-three seventh and was eyeing another birdie when the horn sounded to stop play with thunderstorms circling.
Lee returned and, after birdies on the 13th and 16th, was sitting pretty at five under through 16 holes when the second round was suspended yet again.
The Australian is two shots behind overall leader Scheffler (11 under), having been co-leader at the halfway point of The Players before stumbling in windy conditions to finish in a tie for 20th.
The Perth product is well placed to challenge for his maiden PGA Tour title, having banked four top-20 finishes in six events season.
Lee's form, in his final event before the Masters begin on April 10, bodes well for the first major of the year.
But defending Masters champion Scheffler, whose early-morning 62 equalled the course record he already shared, looms as an imposing obstacle for every rival at Augusta.
"I felt like I was hitting so many good putts, especially at The Players, putts that were going around the edge," Scheffler said after four birdies each on the front and back nine.
"Today was a day where I felt like my ball-striking could have been a bit better and I was able to hole some putts."
It was the American's second-straight bogey-free round as he surged to take a one-shot lead ahead of Canadian Taylor Pendrith, who had back-to-back rounds of 65.
Australian Jason Day (66) moved into the reckoning at four under, while Karl Vilips (one over through 15 holes) and Aaron Baddeley (equal par through 15) are both currently outside the projected cut line.
Rory McIlroy left it late to jump inside the cut line, with three successive birdies from the 16th lifting him to four-under par.
