The 20-year-old Belgium international, who should be part of their World Cup squad in Brazil, was stretchered off after team mate Gareth Barry clattered into him midway through the first half as Liverpool scored their opening goal.
"We're going to assess it," manager Roberto Martinez told reporters after the game.
"At the moment he's got his ankle in a cast and it doesn't look too good.
"He just collided with Gareth Barry at the corner as the ball was delivered into the box. It's there where he twisted his ankle."
Everton endured a tough night at Anfield where they suffered their worst mauling in a Merseyside derby since a 5-0 defeat at Goodison Park in 1982.
Lukaku, on loan from Chelsea, has had a good season for the Toffees and is their top scorer with nine league goals so far, although he has only found the net once in his last 10 appearances in all competitions.
If he is fit he should be in Belgium's squad for the World Cup where the highly regarded team face Algeria, Russia and South Korea in the opening group phase.
(Reporting by Mike Collett; editing by Amlan Chakraborty)
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