In an interview with the Everton website that has subsequently been removed, Lukaku said he didn't believe Anelka should be banned for supporting French comedian Dieudonne M'bala M'bala.
Lukaku said: "He's been my idol since I was a kid. He still is. I think he shouldn't be banned for that [quenelle]. He was just like supporting a stand-up comedian in France. We don't have to make such a big deal about it.
"He's an adult. I hope he doesn't get suspended because he's a player people want to see play on the pitch."
West Brom's French forward is considering his options after being charged with an aggravated offence by the FA over his controversial 'quenelle' goal celebration.
The quenelle has been described as an inverted Nazi salute, and was created by French comedian Dieudonne M'Bala M'Bala, who has been prosecuted for anti-Semitism. Anelka is a friend of Dieudonne's and the player has insisted his salute was a gesture of support and aimed at the French establishment.
Anelka has denied the salute was anti-Semitic, but Jewish groups say if the charge is proved then the 32-year-old's lack of contrition should lead to an even more severe sanction than the five-match ban introduced by the FA this season as a minimum punishment for aggravated offences relating to ethnic origin, race or religion.
West Brom said in a statement: "Anelka has received a 34-page document explaining the allegations against him and informing him that he has until 6pm on Thursday to respond. The player is now considering his options.
"Under FA rules, Anelka remains available for first-team selection until the FA's disciplinary process has reached its conclusion. Following this, the club will conclude its own internal enquiry."
The FA brought in an academic expert to help decide on whether charges should be brought and has spent several weeks working on the case due to its sensitivity.
A three-man independent regulatory commission will now be appointed to deal with the case - either to decide on the sanction if Anelka admits the charge or to hold a disciplinary hearing if he denies it.
The incident happened after Anelka scored during the 3-3 draw at West Ham on December 28.
An FA statement said: "It is alleged that, in the 40th minute of the fixture, Anelka made a gesture which was abusive and/or indecent and/or insulting and/or improper, contrary to FA Rule E3.
"It is further alleged that this is an aggravated breach, as defined in FA Rule E3, in that it included a reference to ethnic origin and/or race and/or religion or belief."
Football's anti-discrimination group Kick It Out, which has expressed frustration over the length of time taken to decide on the case, called for a swift conclusion.
A statement said: "The FA has previously demonstrated its commitment to taking effective and swift action to deal with all forms of abusive conduct in football, and has spent a longer time than desirable in order to give careful consideration to the allegations made in this case.
"Kick It Out hopes that this matter can now be quickly concluded."
Meanwhile, Mark Gardiner, director of communications for The Community Trust, who work to prevent racism and anti-Semitism in football, welcomed the charge for Anelka.
"Certainly we welcome the FA charging Nicolas Anelka, and with it being aggravated behaviour the FA quite rightly has a zero tolerance in response to racism anti-Semitism and this gesture needs to be included in that," Gardiner said.
"We think it is a very serious matter and it should have an extensive sanction including a many match ban.
"But in this context Nicolas Anelka has introduced a very ugly fake gesture into British football and into British society and we now run the risk of anti-Semites making this gesture against British Jews which is a terrible situation to be in.
"I think that Nicolas Anelka is in support for his friend makes matters worse, Dieudonne M'bala M'bala has a string of convictions for anti-Semitic behaviour.
"In November he was fined 28,000 euros for a song that derides the holocaust and mocks victims of the holocaust and then December more charges were laid because he said a Jewish journalist reminded him of gas ovens, so saying this makes matters worse.
"There is no doubt that we wish action had been taken sooner but this was at the beginning a complicated matter but everyone now knows what the gesture means and the FA's action is appropriate."
He is making a habit of saying naïve things publicly- ted maul