The Belgium international found the back of the net twice against Hull on Saturday on his first appearance since turning down the offer of a new contract at Goodison Park.
The 23-year-old still has two years left to run on his current deal with the Merseysiders but there is already growing speculation the Premier League's topscorer could be sold at the end of the season, with Chelsea and Manchester United interested.
Koeman says he does not expect Lukaku's performances to drop just because of his contract situation and says he will be doing all he can to convince the striker to commit to his project at Everton.
"Everybody loves Rom because he's really that key player, the top scorer in the team and he showed that today," Koeman told Sky Sports after the 4-0 win over Hull City.
"Maybe you can stop him for 85 minutes but when it is 11 against 10, even when it was 11 against 11, if he gets space and if they make the kind of mistake for the fourth goal then he will punish that. That's one of his big qualities.
"Of course, we would like to keep the best players because we think we are in a good direction in this project and you don't sell your best players."