The Red Devils currently boast one of the most talented lineups in their history, featuring players who turn out for some of the biggest clubs in the world.
However, the national team has failed to get past the quarter-final stage at both the 2014 World Cup and Euro 2016.
Belgium have made an impressive start to their campaign in Russia with two high-scoring wins from their first two Group G games, which has put them top of the standings.
Lukaku, who is joint-top scorer at the finals on four goals alongside Portugal's Cristiano Ronaldo, is nonetheless eager for the team to also have fun at the tournament.
"This might be the last tournament for our generation because a few players are going to retire so we're playing for them and trying to leave a bit of history," the Manchester United striker told BBC Sport.
"In the last tournaments that we played, we set the bar so high then we didn't reach our objectives. Now we're just trying to enjoy it.
"That's the most important thing. Football is all about having fun - but playing to win at the same time. When you find the right balance there's so much more to enjoy."
Lukaku is doubtful for Belgium's final Group G game against England due to a knock, and will be monitored over the coming days.