3. Lukaku is statistically more clinical than Kane having only had 59 shots to Kanes 141. The service is definitely the difference. Lukaku has 5 assists to Kanes 1. He is not perfect but is not letting the team down.
Those stats are really surprising because Kane is quite clearly a better player, and seems more clinical in front of goal.
According to the premier league website, Lukaku has had 66 shots and Kane 141. Lukaku has 11 goals and Kane 21. So that's 6.7 shots per goal for Kane, and 6 shots per goal for Lukaku.
However, it's also key to look at the stat "Big Chances Missed". Lukaku is showing 10 this season, and Kane 9. Kane has had more than double the amount of shots so I think that shows Kane is shooting from tougher areas far more often, and that makes sense - scoring from tight angles is one of his key skills.
Having said all that, I agree with you really, I don't think any of the issues you're discussing really come back to Lukaku. The guy gets goals, he has a great track record. When the team's playing well, he will score, when they're not playing well, he won't, simple as that really. Same as Lacazette for us. When we suck like yesterday, he's not really in the game. When we're playing well, he scores.