Green (two under) and Lee (even par) will continue their quest to become the first local to win the open in a dozen years in the second round at Adelaide's Kooyonga Golf Club.
Welsh leader Darcey Harry (six under) tees off on Friday with a one-shot cushion from Germany's Alexandra Fosterling, with Kelsey Bennett the best-placed Australian in a batch at three under.
Green was content with her opening round in tricky winds as she seeks to become the fourth Australian winner of the open.
The most recent local to salute was Karrie Webb, who captured her fifth open title in 2014, following wins by Jane Crafter (1997) and Jan Stephenson (1977).
"Obviously if an Australian wins, it's going to be a big deal so it's hard to not really think about it," Green said.
"But now that balls have actually been in the air, it's something you just don't think about.
"There's still lots of good European players so I have just got to focus on what I'm doing myself and hopefully be in contention on Sunday."
Triple major winner Lee, who signed for an opening 72 despite lamenting inconsistent ball striking, concurred.
"I try not to think about it but I know they would love an Australian to be the next winner," she said.
"But there's a lot of golf to be played and you can't really get too far ahead of yourself anyway; so just one foot in front of the other."
Another Australian major winner, Grace Kim, shot three over on Thursday in tough afternoon winds and, in the same group, her compatriot Steph Kyriacou carded a nine-over 81 marred by two quadruple bogeys.Â
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