Belgium could book a place in the last 16 of the tournament on Sunday afternoon with a win against Russia.
"I hope the England fans support us now," said Lukaku.
"We are all proud that we play in such a beautiful country and that we have helped English football to become better. So hopefully the English will now support us throughout rest of the World Cup."
The Belgium squad includes 12 Premier League players, but they have not appeared in a major competition since back in 2002.