Rotorua golfer Lee, the US amateur champion, is one shot off co- leaders American Anthony Kang and Irishman Damien McGrane.
Lee is on nine-under par after rounds of 67 and 68, in a three-way tie for third,
Highly-rated American Anthony Kim, the tournament favourite, loomed a shot further back after signing for consecutive rounds of 68, while Briton Colin Montgomerie was in a group of 13 on seven-under.
Ranked the world's leading amateur last year, Lee's charge looked to have stalled late in his round when he double-bogeyed the par-four 12th to slip five shots off the pace.
But he regained his composure to birdie holes 14, 16, 17 and 18 in a highly impressive finish.
Other New Zealanders who did not fare so well were Michael Long and David Smail, just making the cut at three-under, seven shots off the lead, with Long recovering from an opening round 74 with a 67.
Defending champion Mark Brown of Wellington missed the cut by three shots, while Josh Geary was two shots behind Brown.
