Lukaku highlighted the foolishness of Chelsea's decision to loan him out for the season - Martinez confirmed he cannot be recalled - by inspiring Saturday's 3-2 victory at West Ham.
Leighton Baines may have struck a pair of terrific free-kicks, but it was the half-time arrival of Lukaku that transformed Everton and the 20-year-old crowned his debut with the winner six minutes from time.
A muscular but skilful presence on the pitch, the Belgium striker is equally formidable in his commitment to becoming the best.
"It's true that I watch every single game in the league - 90 minutes. I take my time to study and to learn other strikers' movements and to learn about other defenders. I take my time," Lukaku said.
"Really I want to be one of the best in this league so you can only learn from the best by watching the best. After training I go home and record every game. I have a satellite and I just watch the games.
"My aim is to go down as one of the greatest. That's why I'm at Everton. I'm here to help the team, the team is here to help me."
If the events at Upton Park are anything to go by, Everton should reap the rewards of what could be one of the summer's most productive transfers.
Martinez has been particularly struck by the intelligence of a player who speaks six languages - Portuguese, Spanish, French, Dutch, English and a native tongue in Ghana.
"Romelu is a thinker. He's a really knowledgeable man who looks at games in a very different way and is like a manager in the way that he looks at movement," Martinez said.
"When you have got that at 20, it's incredible. He has had incredible experiences and he's more mature at 20 years old than most and that's difficult to find a comparison.
"He has power, pace, really good hold-up play and on top of that, he has an understanding of where to run and where to play. I've been extremely impressed by Romelu.
"He is intelligent on the pitch and off the pitch. He speaks about games that he's seen, different moves and not the normal conversation that you would have with an ordinary 20-year-old footballer, believe me."
Chelsea were expected to keep Lukaku but Demba Ba's decision to stay at Stamford Bridge on the final day of the transfer window forced a rethink that resulted in a three-way scramble between Everton, West Ham and West Brom.
Everton came out on top after Lukaku identified Goodison Park as the best place to develop.
"Everton were that step I needed. As a team they are always close to the top four and get to cup finals. That was really interesting for me," he said.
"Every time I played against them I had difficult games so I wanted to play in that team. After the top teams I think they are the best team in the league.
"At my age the most important thing is to play and develop. Everton gave me the opportunity so I'm very happy to be here. Chelsea is the future."