He is the first Everton player to score more 20 or more league goals in a season since Gary Lineker banged in 30 in the 1985-86 season.
Lukaku moved two clear of Tottenham's Harry Kane on 21 goals in the hunt for the Premier League's Golden Boot award with a stoppage-time brace at Goodison Park, adding to earlier efforts from Dominic Calvert-Lewin and Enner Valencia.
Lukaku netted twice at the weekend against Hull, but his future at the club has been the subject of speculation after he turned down a new contract offer last week.
Everton are planning a £50million double transfer swoop as they plan for life without Romelu Lukaku.
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Both times the 23-year-old confidently beat goalkeeper Eldin Jakupovic, showing his questions over the club's ambition and refusal to sign a new contract have not affected his appetite for goals. "Of course we like to keep our best players and we will do the maximum. but the final decision will be with the player himself".
Koeman says he held talks with Lukaku on Thursday and told him he was unhappy with the interview, for which the Toffees boss did not rule out disciplinary action.
"We kept the momentum". "You like to be confident, you like to be comfortable at home, you play for the fans and that's really good". But it gave us more space to kill the game and we did that. The Belgian can finish, but his touch isn't great and he doesn't make the kind of selfless runs which would benefit our other attackers - like Roberto Firmino - for example.
"It is all about Liverpool away and Man United away but I am happy we have a chance to climb the table".