Green grabbed a share of the opening round lead with American Stacy Lewis following a bogey-free 6-under 65 at Wilshire Country Club while Lee was also without a bogey and sits alone in third after a first round 66.
Green - who is chasing a maiden win on the LPGA Tour - caught fire through the middle of her round, carding six birdies in a nine-hole stretch beginning at the par-four sixth.
"I holed a six-footer on the first hole for par and I really think that just set the tone for the rest of the round," Green told LPGA.com after her morning round.
"Really happy to be bogey-free, it's probably the first time in a long time that I've had bogey-free so hopefully I can keep that up."
"I think the early tee time helps; I was second group out today so I had fresh greens, not really any wind to worry about so I think that definitely helped but I just felt like my game has been trending for these low rounds so it's nice to pull it off.
"I feel like my game has been trending towards these low rounds" -- @hannahgreengolf following her opening 6-under 65 @lpga_la. She's currently tied at the top of the leaderboard with Stacy Lewis ==> pic.twitter.com/LjzURXTk2X— #DriveOn (@LPGA) April 25, 2019
"I must admit, I holed a lot of putts and I kind of sneaked a couple in that maybe shouldn't have but you've got to take them while you can. It's not easy, especially with the poa in the afternoon, it might get a little bumpy.
"It was just nice to have some confidence and feel like the hole is, you know, a foot wide instead of three inches."
World No. 4 Lee's five birdies were spread evenly throughout her round, at the first, fifth, ninth, 13th and 18th.
It presents yet another chance at victory for Lee who has recorded a trio of top-3 finishes this year including a T3rd result at last week's Lotte Championship in Hawaii.
Queenslander Sarah Jane Smith is also in the hunt in LA, opening with a 68 to be one of eight players at 3 under.
Katherine Kirk was the next best Australian, firing an even par 71 while Su Oh opened with a round of 73.
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