Both players are 16-under 200 through 54 holes and lead Sweden's Johan Edfors (68) by two strokes heading into Sunday's closing 18 holes at Baltray's County Louth Golf Club.
The 22-year-old Lowry, the 16th-ranked amateur in men's golf, gained a large home following by shooting 10-under 62 during Friday's second round.
"A 71 was respectable enough and I'm still in the lead, so I can't ask for any more," Lowry said on the European tour's Web site after being one of only seven to shot a sub-par round Saturday.
"I was happy for him that he was playing well, but I am concentrating on trying to win a tournament," Rock said.
Three golfers -- England's Nick Dougherty (73), Rock's countryman, Scotland's Alastair Forsyth (71) and Thomas Levet (73) of France -- all are 10-under 206 to tie for fourth.