Green carded a two-under 70 while Lee finished even par amid swirling winds at Adelaide's Kooyonga Golf Club on Thursday.
Welsh player Darcey Harry posted a stellar six-under 66 to be clubhouse leader, a shot ahead of Germany's Alexandra Fosterling, with Australia's Kelsey Bennett among a pack at three under.
Bennett's 69 featured five birdies, while 18-year-old South Australian amateur Raegan Denton's three over was highlighted by a hole-in-one on the 149 metre par-3 seventh.
World No.9 Green, who fired five birdies but also three bogeys in a group also including Lee, was satisfied with her first-up performance.
"It was tricky," Green said.
"Collectively as a group we struggled with some of the pin positions just to get it close, but also, once we were on there, to actually read the putt correctly.
"I felt like it's been a while since I've hit some putts and completely misread the putt.
"But I'm pretty happy with two under par. It's very easy to make bogeys out here."
Triple major winner Lee was less content with her round, punctuated by a double-bogey and two bogeys amid four birdies.
"I didn't hit it to the best of my ability, so hopefully tomorrow I can get something going a little bit better," the world No.4 said.
"My ball striking was a bit shaky here and there.
"But my putting was good, my short game was good, so if I can tidy it up a little bit in my long game, then I should be in a good position."
Lee and Green are among 31 Australians in the field hoping to become the nation's first winner of the Open since Karrie Webb's fifth title in 2014.
But the decorated duo were outshone by compatriot Bennett, who last weekend triumphed at the Australian Women's Classic in her home state of NSW for her biggest win, and first victory on the Ladies European Tour.
Another Australian major winner, Grace Kim, was one under through three holes after teeing off in the afternoon.