The 17-year-old had a massive task handling the Belgian.
Lukaku then missed a penalty before West Ham's stunning comeback.
West Ham ended up winning the game 3-2.
Michail Antonio scored his third goal in as many games to start the fight. His header was then followed up by a nod in from substitute Diafra Sakho for 2-2 before this season's star player Dimitri Payet earned the Hammers a win.
Lukaku had given them the lead after escaping the attention of talented West Ham teen Reece Oxford.
The 17-year-old started the game at centre-back with the likes of James Tomkins, Winston Reid and James Collins all out injured.
It was a steep learning curve for the teenager, who tweeted about it after the game:
The West Ham star made a mistake in his dealing with Lukaku from the first goal.
He got too close to the Belgian, who rolled him before slamming the ball home.
But as the game went on he looked better and better up against the talented Everton striker.
It was another great learning experience for the young defender and one that should help him going forward.