Lowry, the home favourite, closed in on a first individual title since 2022 after shooting a five-under-par 65 at the Trump International Golf Links and Hotel in Doonbeg, with Dane Jacob Skov Olesen in second.
Chilean Joaquin Niemann was seven shots behind Lowry, who excelled with his putting on the back nine to move to 16 under overall as he chases only his second Irish Open title.
"I thought if I could shoot a good score I could pull myself away a little bit," Lowry said.
"I feel like I did a good job on the back nine. I felt like I stayed in the fight the whole day and I did some great work on the back nine and I'm very proud of myself.
"It's a big day for me tomorrow. I'm going out leading my home tournament and it would mean the world to me to knock this one off.
"I'm going to have to put my head down, get back to work whenever my tee time is tomorrow and give it a run."
McIlroy's four-over 74 saw him finish the day in a tie for 50th, all but ending his bid to win the tournament for a third time.
The 37-year-old was on the third hole when Air Force One flew overhead, with Trump arriving to watch the action having travelled to Ireland for a two-day official and sporting visit.
McIlroy confirmed he would be attending a dinner with Trump, who owns the course and applauded the world No.2 at the 18th.
When asked about the President's arrival, McIlroy told reporters: "I guess that's not the experience we're used to in a way. I think it's Air Force One's maiden voyage, so that was pretty cool.
"Cool to sort of see all that going on. I was trying to avoid making doubles at that point, so I was trying to concentrate on my own stuff as well."
