The world No.48 is joint 10th at six under the card after following up his opening-round 71 with a 65.
Fellow Australians Cameron Davis (68) and Karl Vilips (70) are at two under and one over, respectively.
Lee, the 27-year-old from Perth chasing a sixth professional win and first since March 2025, trails leader Ryo Hisatsune by five strokes.
Two Japanese players made the most noise on another warm day at TPC Scottsdale's Stadium Course on Friday.
Two-time Phoenix Open champion Hideki Matsuyama had a run of six straight birdies to shoot 64 in the morning wave to take the lead at 10 under.
He was surpassed by his countryman in the afternoon.
Hisatsune (63) was at five under after two birdies on the front nine, then electrified the rowdy crowds by going six under in a five-hole stretch — highlighted by his chip-in at 17 — to reach 11-under 131.
"It was very lucky," Hisatsune said through an interpreter.
"A nice tee shot, but I kind of a pulled it little bit into the water. Some more reset and make it, (so) going to be more fun."
Hisatsune, 23, tied for second at Torrey Pines last week after missing the cut in the season-opening Sony Open. He had four top-10s as a PGA Tour rookie last year.
Overnight leader Chris Gotterup shot 71 to join fellow American Pierceson Coody (68) in a tie for third at eight under.
Top-ranked Scottie Scheffler (65) closed out with a three-foot birdie on 18 to extend the PGA Tour's longest cuts streak to 65. He was seven shots back at four under.
"Felt a bit lost out there at times yesterday, so today felt a lot better, felt more in control of my game," he said.
"You can obviously see that through the cleaner card today."
Two-time champion Brooks Koepka (69) had a much tougher go of it, finishing at two over to miss the cut in his second tournament since being reinstated by the PGA Tour.
With AAP.
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