Marc Wilmots' men attacked from the off in Bordeaux on Saturday as they looked to bounce back from defeat to Italy in their opening fixture, and they did just that in stamping their mark on the tournament with a dominant display.
Lukaku struck the breakthrough after 48 minutes, superbly capitalising on Kevin De Bruyne's burst forward on the counter by picking out the bottom corner from 20-yards, before midfielder Axel Witsel's header made it 2-0 just 12 minutes later.
Everton striker Lukaku got his second, and the Red Devils' third, of the afternoon at a sun-soaked Nouveau Stade de Bordeaux to complete the scoring with 20 minutes remaining as he kept his composure to finish from Eden Hazard's lay-off.
The 23-year-old, whose brace was enough to make him the Euro's joint-top scorer so far this summer, was subject to widespread criticism after their loss to the Italians in the first round of Group E matches, but demonstrated his immense talent to help sweep the Irish aside.
We must keep improving says Lukaku
Speaking in the aftermath of their first win in the competition since Euro 2000 - and their biggest margin of victory since Euro 1970 - Lukaku insisted: "I think we played well in attack and we played well in defence. We did what we needed to do, we needed the three points and we got them, playing very well."
Lukaku, who extended his international record to 14 goals in 46 caps with his sixth goal in his last six appearances, declared that the result "was also convincing" and said they "can only be positive" looking forward.
Acknowledging their underwhelming defeat to Italy, Lukaku labelled them "a very good team with a fantastic coach" and admitted that although it was "a bit of a setback" for the team, it "woke us up" for their second group game.
"Today everything we did on the ball was good, our defence was solid and we forwards did what was expected of us," insisted Lukaku, who called it "all positive" and said that they must "make sure" that Belgium "only grow during the tournament" and "keep playing better and better."
The Belgians moved to second after overcoming Ireland, needing just one point against Sweden in Nice to ensure their progression to the last 16.