And the Spaniard feels fitness was exactly the key issue when the 22-year-old was on loan at West Brom.
Lukaku made a notable impact at the Hawthorns when he was with the Baggies, scoring several classy Premier League goals. But he often didn't last the full 90...
Martinez is quoted as telling reporters: "When he was at West Brom, he had that incredible scoring ratio, but I think he lasted 90 minutes only about seven times.
"For a young player, until you go the full 90 minutes without losing the power and the pace in every action, it’s a long process. Now, it’s very rare for him to finish the last 10 minutes without the same power, pace and control.
"And on top of that, he can play three games in a week - which is quite remarkable for a player of that size. From January, he’s been the mature Rom who can play 90 minutes."
As Opta stats show, only one man has scored more Premier League goals than Everton's Lukaku this season.
That man is the in-form Jamie Vardy, while Leicester City team-mate Riyad Mahrez is the only other forward to have netted as many goals as Lukaku.
The Everton star has certainly grown and matured in recent months, although there may still be a question mark or two about whether he can produce in the very biggest matches against the very biggest teams.
But the Belgian has undoubtedly come on leaps and bounds. For context, former club West Brom have only scored four more league goals than the 22-year-old as a unit all season...