Lukaku scored a stoppage-time penalty which secured Inter a 1-1 draw in Tuesday's first leg of the semi-final between Italy's most widely supported clubs, a game that ended with three players sent off and the two teams at each other's throats.
One of those red cards was for an incredulous Lukaku, who was dismissed for a second booking for his celebrations following his dramatic equaliser, before which he was abused by a small number of home supporters.
The Belgium striker held his finger to his mouth as he has after scoring for his country and told Juve supporters to "shut up" while being mobbed by his joyous teammates.
On Wednesday Lukaku said on Instagram: "History repeats itself. Been through it in 2019... and 2023 again...", referring to when three-and-a-half years ago Inter's hardcore ultras told him that monkey chants directed at him by Cagliari fans were not racist.
It was not initially clear that he had been abused and neither Inter coach Simone Inzaghi (47) nor his Juventus counterpart Massimiliano Allegri (55) mentioned racist chanting while discussing a post-match row which led to Samir Handanovic (38) and Juan Cuadrado (34) also being dismissed and continued as the players headed into the tunnel.
However, Michael Yormark, the president of Roc Nation Sports International, who represent Lukaku, demanded late on Tuesday an apology from Juve for "hostile and disgusting racist abuse" the striker received from some home supporters "before, during and after the penalty".
"The Italian authorities must use this opportunity to tackle racism, rather than punish the victim of the abuse," Yormark said.
Juve said they were working with police to "identify those responsible" while Serie A put out a statement condemning "all instances of racism" after yet another weekend featuring offensive chanting from supporters.
"Serie A strongly condemns all instances of racism and any form of discrimination," Italy's top division said in the statement.
"A few people in the stands can't ruin football and don't represent all the fans at the stadium... Serie A clubs will, as they always have, be able to find the individuals responsible and ban them for life from their grounds."
FIFA President Gianni Infantino (53) offered his support for Lukaku.
"I stand with Romelu Lukaku, just as we do with any other player, coach, match official, fan or participant in a football match who has suffered from racism or any other form of discrimination," he said on Instagram on Wednesday.
"I repeat the call I made earlier this year for fans to stand up and silence the racists.
"Equally, in football, we need to ensure that strict sporting sanctions are applied to address such incidents and to serve as a deterrent."
The head of soccer's world governing body did not address the yellow card that the striker saw as a consequence of his goal celebration.
The incident came on the day Lazio were only given a suspended one-match stand closure for their supporters' mass anti-Semitic chanting during last month's Rome derby.
Dark episodes
The punishment was suspended because of Lazio's efforts in identifying and banning a series of culprits, including one who wore a replica top with the name 'Hitlerson' and the number 88, a reference to the Nazi Germany slogan 'Heil Hitler', on the back.
Lazio's cross-town rivals Roma were also fined 8,000 euros for their fans racially abusing Sampdoria coach Dejan Stankovic (44) on Sunday.
Former Red Star Belgrade, Lazio and Inter Milan midfielder Stankovic was targeted with chants calling him a "gypsy" until Roma coach Jose Mourinho (60) demanded they stop - actions which saved Roma from a harsher penalty.
Lazio have already had the Curva Nord section of the Stadio Olimpico - where their hardcore ultras stand - closed for one match this season following racist abuse at Lecce which left France international Samuel Umtiti (29) in tears.
On the pitch, Serie A has been more exciting over the past few seasons than it has in years, with big clubs like Inter and AC Milan back winning titles in front of packed stadiums and runaway league leaders Napoli playing some of the best football in Europe.
But there have also been a series of dark episodes, including Inter's ultras clearing an entire terrace with force to honour a leading ultra who had been murdered in a gangland execution moments before their team's match with Sampdoria in October.
Napoli and Roma fans were banned from travelling for two months after a mass brawl which held up traffic on a motorway, and Napoli fans fought among themselves on Sunday night while their exciting team were thumped by Milan.
That 4-0 defeat was played out in near-silence as ultras refused to support the team in protest at high ticket prices and a ban on flags, banners and drums they consider essential, leading owner Aurelio De Laurentiis (73) calling them "criminals who we allow to go to games".
