Lee, who only learnt he was playing an hour before the tournament started on Thursday, fired a five-under par 67 to go with a first-round 70 and stand at seven under around the 6,542 metre (7,148 yard) High1 Resort Country Club.
Griffin, five under and in second place overnight, shot a 70 on Friday to grab a share of the lead.
"The last time I was leading going into the weekend was at least a couple of years ago, at the Australian PGA," said Griffin, a natural left hander who plays right-handed.
"I have won since, but never had the lead going into the weekend for a while."
Lee, 25, was born in Korea but spent the last 11 years in Australia where he learnt the game. A professional for just three years, he plies his trade on the China, Korean and Australasian Tours, and the High1 Resort Open is only his second start in a OneAsia event.
"I wasn't really in great shape for this, but I tried my best and it turned out pretty good," he said.
"I'm still finding my way so I hope I can keep this up. Making the field was a result; playing the weekend is a bonus."
Griffin (left) has had just one bogey in 36 holes of golf -- but feels his score could have been even better had a few putts dropped.
"It felt really good out there. I got away to a nice start and made a couple of birdies, and then on the back nine I actually played some of my best golf of the last two days. I hit some putts that looked good, but just didn't go in."
The one billion won (around U.S.$900,000) tournament -- worth three times more than any other regional tour event being played this week -- is the sixth leg on the OneAsia calendar and the second time it has been played in Gangwon-do, which will host the 2018 Winter Olympic games.
The venue doubles as a ski resort in winter and last year the tournament had to be cancelled when fog and low cloud prevented more than one round from being played. The weather is expected to turn for the worse again on Saturday after two days of brilliant sunshine.
Starting a shot behind the leaders will be Australian Scott Arnold (66), who looked destined for the round of the day until a double bogey on the 16th. Joimning him at six under is Kim Bong-jin (71), joint second overnight.
Five others are a further stroke behind, including Australian Aaron Townsend (69) who eagled the par-four fourth when he holed a 25-footer after driving the green.
Townsend, who missed the cut by one at the Open Championship at Royal Lytham & St Annes earlier this year after making the field through International Final Qualifying, has made only two cuts on OneAsia this year -- both in Korea.
"It hasn't been a happy hunting ground for me in the past, but something might have changed," he said.
Overnight leader Jason Kang, who hails from California, remains well in the hunt at four under despite a second-round 74, but with the cut set at two over par, a number of top players were booking early flights home.
Andre Stolz, winner of the Order of Merit last year, was eight over after two rounds, while Michael Hendry's dismal run continued when he missed the cut by one. He has yet to play the weekend on OneAsia this year.
2012 Order of Merit leader Kim Bi-o -- winner of two tournaments this year already -- is two under after rounds of 72 and 70.
Leading 36 hole scores;
After round 2 of the 2012 High1 Resort Open being played at the par 72, 6,542 metres (7,148 yards) High1 Country Club (a- denotes amateur):
137 - LEE Jun-seok (KOR) 70-67, Matthew GRIFFIN (AUS) 67-70.
138 - KIM Bong-jin (KOR) 67-71, Scott ARNOLD (AUS) 70-68.
139 - Aaron TOWNSEND (AUS) 70-69, CHOI Ho-sung (KOR) 71-68, SONG Young-hoon (KOR) 74-65, HAN Min-kyu (KOR) 68-71, LEE Tae-hee (KOR) 72-67.
140 - PARK Sang-hyun (KOR) 69-71, CHO Min-geun (KOR) 69-71, Jason KANG (USA) 66-74.
141 - Rohan BLIZARD (AUS) 70-71, KIM Bong-sub (KOR) 74-67, Marcus CAIN (AUS) 72-69, PARK Ju-hyuk (KOR) 69-72, PARK Jun-won (KOR) 71-70.
142 - KIM Bi-o (KOR) 72-70, KIM Yeong-Su 912 (KOR) 71-71, HUR In-hoi (KOR) 69-73, LEE Jung-hwan (KOR) 70-72, KIM Min-su (921) (KOR) 71-71, MO Joong-kyung (KOR) 70-72, HONG Soon-sang (KOR) 70-72, Daniel FOX (AUS) 73-69, SHIN Yong-jin (KOR) 71-71.