Holmes shot three-under-68 and Lowry shot four-under-67 in Friday's second round at Royal Portrush.
"I'm in a great position, but my God, have we got a long way to go," Lowry said. "There's two rounds of golf on this golf course against the best field in the world."
Neither has ever won a major championship. Lowry finished second at the 2016 U.S. Open. Holmes' highest finish in a major was third place at the 2016 British Open.
"There's a long way to go in this tournament," Westwood said. "If it's going to happen, it's going to happen, and if it doesn't, it doesn't."
The British Open began Thursday and concludes Sunday.