After hitting seven birdies in an opening 66 on Thursday, McIlroy cemented his place at the top of the leaderboard with a birdie at the par-four third.
But the Masters champion hooked an iron into the water with his tee shot on the sixth before dropping another shot on the ninth.
While he scrambled to save par on the long 13th, McIlroy incurred another penalty on the short 14th before bouncing back with a birdie at the 16th by sinking a 45-foot putt for birdie.
Another wayward shot into water on the 17th led to a bogey and the 36-year-old finished with another dropped shot after he failed to get up and down from beside a rock to the right of the green.
Playing with Ryder Cup team-mate McIlroy, Lowry mixed three birdies and two bogeys on the front nine but picked up shots at the 10th and 16th to sit alongside two-time DP World Tour winner Elvira.
“I do quite enjoy it, the artistry of moving the ball around and hitting different shots,” Lowry told Sky Sports.
“We had a great group today. When you’re out there having a bit of fun it’s easier to play good golf so that attitude for the rest of the year and I’ll be pretty good.”
It was a rough Friday for Fleetwood, however, as the Englishman failed to make a birdie or eagle in a round for the first time since the US PGA Championship last May.
England’s Marcus Armitage carded a 70 and is two shots off the lead while South Africa’s Thriston Lawrence – who was third in 2024 – is alongside McIlroy at two under.
