As important for Martinez, who has fought to forge a team from a collection of individual talents, is a lack of ego - something Lukaku himself insists he has understood as he batted away talk of the Golden Boot for the tournament top scorer.
"We're not yet real favourites", insisted Lukaku, who may get a rest against England after taking an ankle knock.
Martinez said Kane's form came as no surprise because he knew the Tottenham man was ready to take on leadership duties in the England camp. It's not every time you go through after two games, so we're happy with that.
But what does Gareth Southgate do when it comes to picking his side for the final Group G match against Belgium, who have also qualified, in Kaliningrad on Thursday? It carries with it the feeling of immediacy, of the need to win something when these players are still within their prime.
Lukaku was hobbling towards the end of his time on the pitch though, and manager Roberto Martinez sacrificed him early in the second half to make sure he is fit and firing for a big clash with the Three Lions on June 28.
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"There's a long way to go and a lot of good players just behind me [on the scoring list]".
Both have already qualified for the last 16 - only the group victor needs to be decided - so Thursday's Group G finale in Kaliningrad provides a rare chance in an unrelenting World Cup schedule to rest exhausted legs, recover from injuries and avoid the risk of suspensions. Another against England would see them suspended for the first of the knockout games.
"It's a game that we can celebrate and enjoy".
He also has back-to-back games with at least two goals. If we play against defensive teams, we have more trouble and people immediately think our play is slower. "I think we are going to win today", said one of Tunisia's fans.
Vertonghen plays with Kane for Spurs, and is Lukaku's global teammate with Belgium, so he knows better than most the the ins and outs of both players' games.