After a goalless first-half, Lukaku managed to score his, and the teams, first goal of the tournament with a brilliant curling finish form the edge of the penalty area.
Axel Witsel got in front of his marker and headed home a second before Lukaku rounded off the scoring with a clinical finish after Belgium broke up field.
The clean-sheet is Belgium’s first at a European Championship since Euro 1988, after the Republic didn’t manage to force Thibaut Courtois into a save.
Belgium will face Sweden in the final game of Group E, with a point enough to see them through, while Ireland must beat Italy, who may rest a number of starters after confirming top spot with a game to play.
Strong start by both sides
Marc Wilmots made three changes to the side that lost to Italy in the opening match, with Laurent Ciman, Marouane Fellaini and Radja Nainggolan being replaced by Thomas Meunier, Mousa Dembele and Yannick Carrasco.
The Red Devils started the game well, with Kevin De Bruyne looking at his best after a disappointing first match, along with Lukaku.
The Manchester City star caused problems every time he managed to get on the ball, especially from wider positions.
Chances go begging in the first half
After sending in a brilliant cross, which was headed out as far as captain Eden Hazard, the Chelsea man lashed a shot over the bar.
However, the Irish defence looked solid and compact and until that chance, they were virtually untroubled, and on 25 minutes they had a brilliant opening of their own.
Wes Hoolahan latched onto a loose ball and drove forward, but after trying to thread the ball through to Jeff Hendrick, Toby Alderweireld managed to make an important tackle to see off the dangerous attack.
The Red Devils did have the ball in the net, but Carrasco was flagged offside after Darren Randolph did well to parry the initial shot onto the bar before the Atletico Madrid winger headed in the rebound.
Lukaku strikes after half-time
The flag went up and the Irish were given a lifeline, and the sides went in goalless at the break, but that soon changed.
Alderweireld was fortunate not to have given away a penalty for a high boot on Shane Long, but after play was waved on, Belgium went to the other end and scored.
Lukaku sent De Bruyne through down the wing, and the City man passed the ball back across to the forward, who curled his shot into the bottom corner from outside the area.
The Red Devils’ lead was soon doubled on 61 minutes, Meunier crossed into the box, and Witsel headed home unmarked from close-range after he lost his marker.
Confident Belgium take control with third goal
The Irish were down, and a third goal followed the second nine minutes later, James McClean lost the ball near the corner flag and Meunier started the counter attack.
The full-back released Hazard, who skipped past a sliding Callum Clark, and the rest really was history, as he managed to square the ball across for Lukaku, who finished with ease.
O’Neill’s men didn’t have any reply whatsoever and they could have been four down with minutes to play, as Dries Mertens and Christian Benteke linked up well.