Other ties in the round of 16 see Wolfsburg host Inter Milan, Napoli welcome Dynamo Moscow while Fiorentina await AS Roma, with return legs to be played a week later.
The 21-year-old Lukaku is the top scorer in the competition with six goals, mainly thanks to his hat-trick in the away leg and brace at home during Everton's 7-2 aggregate thumping of Swiss side Young Boys in the last round.
"Sometimes you need to remember his age. Despite it he is such a mature goalscorer," said coach Roberto Martinez, whose side has won three of their four European home ties but who lie 14th in the Premier League.
The last time Everton got this far in Europe was 2007-08, when they lost on penalties to Fiorentina, but there is hunger in Everton's attitude that sees them targeting the final in Warsaw on May 27.
On the other hand Dynamo, with two away wins in the Europa League, can count on their striker Andriy Yarmolenko, who has three goals so far in the competition.
Unbeaten in the competition this season, Inter are one of five Italian sides in the last 16, but they face a tough challenge against Wolfsburg who have not conceded a goal in their last three European games and are second in the Bundesliga.
Roma beat Fiorentina 2-0 at home in Serie A this season and drew 1-1 away which will mean Rudi Garcia's side will feel confident after winning their last away game in Europe too.
Holders Sevilla travel to free-scoring Villareal for the battle of La Liga hopefuls. The hosts have scored 20 goals so far in the Europa league.
Dynamo Moscow are in Napoli, knowing their rivals on the night have kept five consecutive clean sheets.
Napoli coach Rafael Benítez has won the competition twice previously in 2004 with Valencia and in 2013 with Chelsea, the last English winners of the trophy.
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