Marc Wilmots' side attracted criticism for the lacklustre showing in their 2-0 defeat to Italy which opened their Group E campaign.
But they looked back to their best in Bordeaux on Saturday as Lukaku's double and Axel Witsel's header left the world's second-ranked team needing just a point from their final game against Sweden to reach the last 16.
There had been talk of unrest among the squad heading into the Ireland game – something Lukaku suggested was at least partly true – but the Everton striker believes clear-the-air talks on Thursday improved the situation.
"I'm very calm; the team as well," he said in quotes reported by UEFA.com.
"We had a team meeting two days ago, where everyone could express their opinion and yes, we played well.
"The team responded very well. We did what we had to do, we had to play good football and keep a clean sheet. That's what we did; now on to the next game.
"We're dealing with a lot of personalities and everybody wants to win and players give their all," he told ITV Sport.
"Sometimes there are discussions, but it is normal. Everyone needs to be on the same page. I don't think we were against Italy, but we are now."
Lukaku celebrated his opening goal by running to the bench, where he was engulfed in a bear hug with his coach, but the striker revealed Wilmots was not the man he was initially searching out.
"My brother, Jordan, was on the bench and I wanted to celebrate with him. He's always been there for me so I wanted to thank him for that," he said.
Witsel, meanwhile, dedicated the victory to the nation's supporters, who were out in colourful force in Bordeaux.
"Our objective was to get three points and we need to do the same against Sweden," he said.
"Our fans created the great atmosphere and this win is for them."