United's league record had been perfect until they were held to a 2-2 draw at Stoke last Saturday, although the disappointment of conceding twice was mitigated by the impressive scoring form of Lukaku and Marcus Rashford.
Now 24 and with six years of Premier League experience behind him, Lukaku is now ready to succeed at the top level according to his manager, unlike in 2011 when he joined Chelsea from Anderlecht.
"I think Romelu has come here at the right moment," Mourinho said. "He is a good age. He has a good number of years of experience with different clubs in the Premier League. He is clearly a player who has adapted to the Premier League.
Lukaku's strong start to life at Old Trafford, he has six goals in six games for United, will help to offset the absence of France midfielder Paul Pogba, who may be out for several weeks.
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Pogba's hamstring injury, sustained in the early stages of Tuesday's 3-0 Champions League victory over Basel, will certainly keep him out of Sunday's match, and there is no guarantee that he will be available for France's decisive World Cup qualifiers against Bulgaria and Belarus in October.
Phil Jones and Eric Bailly are set to return in central defence, having missed the win over Basel through suspension, while Antonio Valencia should be restored at right-back, having made way on Tuesday as Ashley Young played for the first time since recovering from a summer operation on a hamstring problem.
- Koeman meeting -
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Wayne Rooney's return to Goodison Park from United -- replacing Lukaku -- has not gone as well as the Belgian's move despite scoring in his first two league matches this season.
Everton manager Ronald Koeman revealed he would hold a meeting with his senior players to try to get their season back on track before the trip to Old Trafford.
Koeman planned to get Rooney, Leighton Baines and Ashley Williams, among others, together at their Finch Farm training base in the hope of getting a reaction against United.
"I will have a meeting with most of the players, with the key players," Koeman said.
"It's time for the experienced players to stand up. I am worried about what I saw against Atalanta. It was a wake-up call.
Koeman, who has no fresh injury concerns before the match, warned that Lukaku could tear his team apart if they do not improve dramatically at Old Trafford.
"We know him really well but he's one of the best strikers," said the Dutchman.
"I said several times last season he is a real finisher. I know how we have to defend against him. There are a lot of qualities. He is dangerous in the box and fast and strong. If we are defending how we defend in the last few games it will be his afternoon.