Lukaku joined the Toffees on a season-long deal on transfer deadline day in what many regarded as a surprise move.
The Belgium international scored 17 goals for West Brom in the Barclays Premier League while on loan with them in 2012-13 and it had been widely expected that he would go on to feature prominently for Chelsea, who he signed for in August 2011, in this campaign.
But the conversations he had with the London outfit's manager Jose Mourinho about his first-team prospects convinced Lukaku that he would be best off - particularly with a view to next summer's World Cup - going out on loan again.
And asked if he felt he had a point to prove, the 20-year-old said: "Yes, because I think after last year, I deserve a chance - like I did the year before, before I went to West Brom.
"I thought I deserved that chance, I went to West Brom on loan and did well.
"This year, I have a point to prove first to myself, that I can do it again, and then to Chelsea, to show that I can be number one over there as well."