The 20-year-old striker is due to see out the season at Goodison Park having completed a loan switch from Chelsea last summer.
He has enjoyed a productive 2013-14 campaign, netting 14 times in all competitions.
The latest of those came in a crucial 3-0 victory over Arsenal which lifted Everton to within a point of the Champions League places.
Roberto Martinez's side still hold a game in hand on the fourth-placed Gunners, suggesting a return to European football's top table could be on the cards, and Lukaku is determined to ensure that he signs off this summer having left a lasting impression on the blue half of Merseyside.
He told the Liverpool Echo: "For me that's my ambition, that's why I play football now - to make history and leave my mark wherever I go.
"At this moment, that's my drive. I'm a fierce competitor and I want to win every game on the run-in.
"I've said since I came back from my injury I'll do anything that I can to help the club qualify for the Champions League and do well in the cup.
"We didn't succeed in winning the (FA) Cup, but in the league I think we're all good."
Were Everton to break into the top four, Martinez would be expected to step up his efforts to land Lukaku on a permanent basis.
The Belgium international is, however, reluctant to speculate on what the summer transfer window may bring, with his focus locked on the end of the current campaign and a World Cup adventure in Brazil.
He added: "I'm trying not to look too far ahead for now.
"I'm still two years under contract at one of the biggest clubs in the world.
"This is a team that is growing and for me, I just want to help Everton instead of thinking about myself and the next step.
"There are so many things on the horizon - like big games against Man United and City, then the World Cup - so I have to give it a place in my head but not focus on it.
"For now, it's just helping Everton finish fourth and then we'll see."