Lee, a former winner of the event, recorded an opening round of 70 to be tied for 11th and just three shots from the leader and world number one, Shanshan Feng.
Lee finished her round with three consecutive birdies in her last four holes after a series of bogeys had seen her slip to 1 over par.
Green, in her rookie LPGA Tour season, had moved to 1 under par but a bogey at her last hole of the day (her 9th) saw her in a share 22nd place at even par.
Lee won this event in 2016 to record the first of her three LPGA Tour titles.
Off the back of three top tens in five starts in 2018, the Perth native appears well place to contend once again.
Green is currently in second position in the Louise Suggs Rookie of the Year title mainly as a result of her 3rd placing at the Women’s Australian Open in Adelaide in February but an impressive 16th place in her first major championship appearance at the ANA Inspiration was also a further indication of her talent.
Katherine Kirk, Rebecca Artis and Sarah Jane Smith opened with rounds of 73 but for Victorian Su Oh her woes continued with a round of 77.
Feng leads by one over former Gold Coast-based South Korean Haeiji Kang, Sweden’s Martina Edberg and Canadian Brook Henderson.
SWING LIKE RICKIE FOWLER
Want video tips delivered straight to your inbox? Subscribe to iseekgolf.com newsletters.