The Belgium international took his tally to three goals in just 135 minutes of league football after scoring twice in the 3-2 win at home to Newcastle which extended the only remaining unbeaten record in the top flight.
Lukaku has made an immediate impact since arriving on a season-long loan from Chelsea but he refuses to get ahead of himself.
"Hopefully it is one of many good performances," he said.
"Every game I have a simple approach: to do my best for my team and then everything comes automatically.
"The next target is Saturday (against Manchester City).
"I'm very happy with the way things are going."
Lukaku said there was still plenty of work to be done, especially after seeing their comfortable 3-0 half-time lead pegged back by the visitors after the break.
"Something we have to work on is to kill games easily and stop the threat and then we can do better but the season is long," he told evertontv.
"We are playing well and we have to profit from it, everyone in the team has to.
"We have a very good squad and I think everyone can be important in this team.
"Hopefully we can continue this form and better results will come."
The victory - the third in succession after a trio of draws - moved the Toffees into fourth place.
Manager Roberto Martinez is pleased the changes he has made since taking over from David Moyes in the summer are coming to fruition but he was reluctant to get involved in predictions about the challenge for the top four and title.
"It is a good start. We were very disappointed with the return we had in the first three games," he said.
"We deserved a lot more but what has pleased me is that we have been very consistent in our performances.
"It (title race) is really open. There are many changes from a manager's point of view and I don't think it will shape up until the first third of the season gets settled.
"But it is really good to see five or six teams capable of winning games.
"I think the competition will be one of the best for a long time."
Unfortunately for Newcastle their concerns are currently in the other half of the table as just seven points from six matches have left them in 16th place.
Manager Alan Pardew believes that is a false position, however, and is targeting a return to the top half.
"I think we still have a chance of the top 10," he said.
"As a team we have shown inconsistencies, especially in our defending.
"Some of the goals we have conceded this year really are not good enough for us.
"The consistency of performance individually and as a unit - the back four - we will have to do some work and there will have to be some personnel changes in there.
"I thought Mike Williamson came on and we looked a lot stronger and he has given himself a great chance of featuring at Cardiff."
At 3-0 down Newcastle's fans sang 'We want our money back' but Pardew hopes the second-half performance will have restored some faith.
"With the fans travelling all that way and seeing some of the defending in the first half I can understand it," he added.
"But I hope at the end they see they have something to cling on to in terms of the pride we showed in the shirt.
"It wasn't just about digging in and making some tackles, we showed some quality in the second half and that will serve us going forward."