The Northern Irishman is level on 16 under par with Ryder Cup team-mate and playing partner Viktor Hovland.
Lowry eagled the ninth and 10th holes, only for three bogeys to drop him back down the leaderboard.
McIlroy led the way alongside playing partner Viktor Hovland on a day of low scoring.
Fleetwood shot a 66 to sit on nine under par.
The 35-year-old golf instructor had hoped to earn a place in the field by right but failed to get through. That all changed on Friday eve...
The world number 25 revelled in the sunshine and lack of wind to make six birdies in a front nine of 30.
The world number 25, who made the halfway cut on level par, revelled in the sunshine with little wind to pick up six shots on the front n...
The Australian leads the Open by two shots from Cameron Young.
The Northern Irishman is three shots off the lead.
The Australian was 13 under to lead by two from Cameron Young with Rory McIlroy and Viktor Hovland a shot further back.