The 39-year-old started the fourth round in 16th place before setting himself up for a strong finish with five birdies on the front nine.
South Africa's Justin Walters was one shot behind Lynn in second spot at the Oceanico Victoria course in Vilamoura, while Stephen Gallacher of Scotland, Austria's Bernd Wiesberger and overnight leader Paul Waring of England finished two behind the leader.
Scotland's Scott Jamieson failed to back up his stunning third-round of 60, suffering three bogies on the back nine for a one-over par 72 to fade to a tie for 13th.
The Scot became just the 17th player to shoot a 60 on the European Tour and went close to becoming the first player to shoot a 'magical 59' when he narrowly missed the cup on the 18th.
(Writing by Josh Reich in London, editing by Ed Osmond)
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