Lukaku has been in scintillating form for the Toffees in 2017, netting 13 goals across eight successive Premier League wins at Goodison Park since the turn of the year.
Everton's struggles on the road were epitomised by a poor display in the 0-0 draw with West Ham last time out, though, and they will face a stern test when Antonio Conte's league leaders visit Merseyside on Sunday.
Key to a positive result for Everton will be Lukaku, whose future at the club remains in doubt, and Koeman believes his side need more players who possess the 23-year-old's attitude if they are to compete with the likes of Chelsea - who beat the Toffees 5-0 earlier in the season.
"I don’t know if he [Lukaku] will stay, we will see what happens at the end of the season," Koeman said.
"We like to keep the best players. Lukaku always wants to show the best of himself. I think we need offensively more players who score more goals because the difference between Lukaku and the rest of the players is too big.
"Maybe we need to change our mentality because I felt a little bit less intensity, maybe less motivation [against West Ham].
"It's always difficult if you have the end of the season feeling. That's what I don’t like."
"It is on the manager to get the motivation out of his side. That is my challenge," the Dutchman, who also claimed that the title race is far from over, continued.
"If we keep the distance between us and Arsenal to three points or less, then the last game of the season is Arsenal away. If not, then you have to find other ways to motivate.
"We had only one game this season that we had no chance, and that was the Chelsea away game, from the start until the end. No chance to get even one point from the game.
"Now we can show that the team is improving and much better and give more in every aspect of football.
"[The title race] is not done. Chelsea and Tottenham have difficult weekends coming, maybe this one will be the decisive one."