I've watched Lukaku quite regularly with Belgium prior to and during the EUROs and I thought him and Hazard were no good fit. Hazard is always looking for quick link up play with sudden passes and one-twos inside crowded areas, and Lukaku simply couldn't catch up. He produced many easy turnovers and bad passes with his back to the goal, often interrupting Belgium's attacking flow.
Whether it was his first touch, his hold up play or his passing under pressure, everything seemed quite unreliable. He reminded me a bit of Mario Gomez: A beast when he faces the goal in dynamic situations and is able to shoot (or pass) within a short amount of time and with space available; But not good enough on the link up aspects for a top team that has to play through a well-organised defense.
Now, I don't watch Everton at all and I have seen people say on this forum that he improved greatly on these issues. That would make my objections obsolete, although I'm sceptical if a player can make significant progress in these areas at age 23.
The difference between 75% and 65% pass success rate is not insignificant imo. Especially if my speculation is right that Chelsea's opponents play more defensively/get pushed back deeper than Everton's, and there is less space around the box. (Just a speculation, as I said, I don't watch Everton.)
In my experience players only benefit from playing with better teammates when they offer a similar basic skillset. I have seen decent/good players struggle quite badly in top teams if they didn't. For Belgium, Lukaku played with Hazard, De Bruyne, Mertens and Carrasco and I don't think the whole setup was really flattering to him.