McIlroy found himself in a share of fifth place after an opening-round of 67 on Thursday, despite running up a double bogey on the 15th when his drive bounced off a young spectator's head and ended up out of bounds.
However, a second round of 75 saw the world number two only make the halfway cut by one shot on two over par, while he then added a 73 in perfect conditions on Saturday.
That meant another early start this morning for the former US Open champion, but any hopes of a late charge up the leaderboard before the forecast strong winds arrived were soon dashed.
After a par on the first - Lytham is the only course on the Open rotation which begins with a par three - McIlroy bogeyed the second, ran up a double bogey six on the third and then dropped another shot on the fourth.
McIlroy steadied the ship with four pars to be out in 38, but Lee Westwood and Ian Poulter were showing that far better scoring was still possible.
World number three Westwood had started with a run of par, birdie, birdie to improve to two over, while Poulter had eagled the par-four second to lie one over.
McDowell shares second place with halfway leader Brandt Snedeker on seven under par, four shots behind Scott, with Tiger Woods another shot back in fourth.
After three days of calm conditions, strong winds are forecast with gusts of 25 to 30mph expected to develop, with isolated gusts of 35mph possible after 3pm.
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