"It leaves a little sour taste. I played 17 and a half great holes," Dyson said. "I could be out of sight to be honest. I've chucked some shots away, but everybody is going to say that."
After a two-hour delay due to a waterlogged course and in windy conditions, Dyson shot a one-under-par 71 to move to five under and take the lead from Gregory Bourdy.
The Frenchman, who shot 73 and 66 in the first two rounds, suffered a meltdown in recording 80 to fall to joint 21st.
Spain's Pablo Larrazabal and Dane Soren Kjeldsen are a stroke off the lead.
Larrazabal shot 69 at his home tournament, which celebrates its 100th anniversary this year. Kjeldsen managed a 71.
"Only one bogey - it's a great round," said Larrazabal. "I like it when the course is challenging. I don't like it when the winner is 25 under."
Dyson - the current Irish and Dutch Open champion and highest-ranked player in the field at number 36 in the world - would move into a Ryder Cup qualifying position should he win. The tournament takes place in Chicago in September.