The Belgium international, on loan from Chelsea, has missed four matches with an ankle injury but his return to fitness could not have been better timed after back-to-back league defeats have left the Toffees 11 points adrift of fourth-placed Liverpool.
Everton went into the Merseyside derby at Anfield, in which Lukaku sustained his injury, on January 28 just a point behind their near-neighbours but have dramatically fallen off the pace after losing that match - not helped by the postponement of a home game against Crystal Palace.
Lukaku, 20, has scored just once since the end of November but comfortably remains Everton's top scorer with nine league goals.
Martinez expects to see a newly-refreshed and determined player when West Ham visit on Saturday.
"As a number nine he is as complete as you are going to get in world football. Something which is a rare breed - to have such a talented footballer having that target man role," said the Toffees boss.
"When you look at his age you are quite surprised by the package he brings.
"When you see him as a player you build a perception of a strong target man who is good with his back to goal and you get such a shock when you speak to him about football.
"He is a very intelligent man who wants to understand the game and I've been very impressed by how he approaches the game.
"He is good in the box as a number nine, attacks the ball well and is a good finisher, but can use the counter-attack with his pace and ball control.
"Romelu has had a terrific season and has a big role to play in our squad."
Martinez admits their recent run of just one win in their last five league matches has dented confidence, especially after last week's defeat at Chelsea when they played well enough to get at least a draw but conceded an stoppage-time goal.
Martinez wants his players to learn lessons from their Chelsea counterparts in terms of getting results when not at their best but is also looking forward to the comfort of a home game.
"It is one of those situations where you feel vulnerable as a team and you need a warm feeling - we get that at Goodison," he added.
"What you saw (from Chelsea) on Saturday was the know-how and experience of how to get results without being the better side and that is a great knack which all the winning sides have and it is important we develop that as well.
"Over a long period you will not play well every single time but it is important if you can get results when the overall performance does not deserve it."
Everton run into West Ham at the wrong time after Sam Allardyce justified his board's decision to keep faith with him by guiding his side to a maximum 12 points in February to ease their relegation worries.
"West Ham deserve huge credit. I have seen it many times, when you get into a negative run it is difficult to be consistent after that," said Martinez.
"From the outside there is always the perception a team having bad results could end up with a manager losing his job but I think a manager worries about what can be done next.
"They have shown that and continuity at the club has paid incredible dividends.
"To see they have conceded only one goal in five games and had four straight wins after a good draw at Stamford Bridge shows they are a team in form."