The Belgian and the Spaniard had their own little personal battle to contend with.
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.
The story of the game was perhaps Lukaku v West Ham goalkeeper Adrian.
The pair squared up to each other early on in the game after Lukaku clattered into the Spanish goalkeeper.
The Belgian then tucked away a delightful finish into the bottom corner to give Everton a lead.
But it was Adrian who had the last laugh in the end. He saved a penalty from the Everton star, although he was five yards off his line when the kick was actually taken. He then made a good stop after Lukaku found himself through one on one with the Hammers star.
So in the end Adrian and West Ham certainly took the bragging rights.