Lynn shot 68 Sunday and wound up 11 under for the tournament. McIlroy had a final-round 67 and was 10 under overall.
Dyson, who won the KLM Open in 2006 and 2009, picked up his second European Tour win of the year. He also won the Irish Open.
Third-round co-leaders Gary Orr and James Kingston slipped Sunday. Orr had a 1-over 71 and ended up in fourth, a stroke behind McIlroy. Kingston was 3-over 73 in the final round and tied for sixth.
Dyson had a pair of birdies and two bogeys through 11 holes but ran off three consecutive birdies with short putts over Nos. 12-14. That put him into the lead and a birdie at 18 sealed the win
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