World No.5 Lee was lying joint-third after a steady first-round 68, but a score of 74 on Friday saw her slump down the order to join a group of nine players sharing 29th place on two under at Dundonald Links in Ayrshire.
Fellow Australian Cassie Porter carded a second consecutive round of 70 and stands two shots above Lee on four under, but eight shots behind leader Wood.
Woad, 21, carded a 7-under 65 on Friday to move to 12-under. She was the No.1 amateur in the world before turning pro after a tied third finish at the Evian Championship two weeks ago.
Korda and Denmark's Nanna Koerstz Madsen both shot 66 in the second round and are tied for second at 10-under.
Sei Young Kim (67) is in solo fourth at 9-under and fellow South Korean Hyo Joo Kim (66) is another shot back in solo fifth.
Woad collected seven birdies during a clean round, including birdies at all four par-5 holes.
"Bogey-free is always nice," Woad said. "Hit a lot of greens ... a lot of fairways, and then holed a few nice putts."
Woad's remarkable month began with a six-shot victory at the Women's Irish Open, which made her the first amateur to win on the Ladies European Tour since 2022. She finished 13-under at the Evian Championship the following week, one shot behind winner Grace Kim.
Woad played the first two rounds with Korda, whose round Friday featured seven birdies and one bogey at the par-5 18th hole.
Korda is still looking for her first win of the season, which includes a T2 at the US Women's Open, as players ramp up for next week's British Women's Open at Royal Porthcawl in Wales.
"I started out strong with two birdies on my first two holes, and then the wind kind of died down throughout the day, so capitalised on the weather," Korda said.
Defending champion Lauren Coughlin (70) is part of a seven-way tie for 12th at 4-under.
First-round leader Charlotte Laffar of England plummeted into a tie for 91st place and missed the cut after a 10-over 82 on Friday.
