Lukaku, the Toffees' highest scorer in each of the last three campaigns, has not netted in 13 matches in all competitions for the club but scored two for Belgium on Tuesday.
When asked ahead of Monday's Premier League trip to Sunderland what he expects from Lukaku this term, the Dutchman said: "I expect a lot.
"He is a very good player and knows that he can improve.
"Of course, he is an important player because he is normally the top scorer of the team - he showed that with Belgium on Tuesday.
"And I hope he will score next on Monday."