Kane is quite a bit technically superior to Lukaku - this means his hold up play is far superior, he's better in the air and he's a better, more consistent passer in and around the box and he's less likely to break moves down by losing the ball. His superior touch and ball control means the ball "sticks" up top much more reliably than it does for Lukaku (part of the reason that United's attacks break down more often compared to Spurs is that Kane anchors so many moves).
Lukaku is a great athlete and he does give you the ability to play on the shoulder of defences in a way Kane does not (though Kane is faster than people seem to think he is), but his inferior hold up play, aerial ability and close control leave him a level below Kane in terms of building an attack. There's a lot of talk about Spurs attack creating more chances for Kane, but he's a huge part of that chance creation as he allows and assists attacks to build behind him, bringing people into play and providing a secure outlet to play the ball up to under pressure.
I actually quite rate Lukaku's finishing ability, and it's close to Kane's imo - both are terrific finishers with both feet and from unorthodox positions. It's the other stuff before the finishing that is what truly separates Kane from nearly any other striker in the world.
Agree with bits and pieces.
Kane isn't better than Lukaku at heading the ball. Before this season, I posted stats for last 2 seasons (2015-16 and 2016-17),
Lukaku won 221 aerial duels compared to Kane's 111.
Lukaku won 40%, Kane 34%.
Lukaku has scored 21 headers, Kane 16.
There isn't a single metric to show Kane is better in the air. Even this season,
Kane 1.8 aerial duels per 90 mins while losing 2.3,
Lukaku 3.8 aerial duels, losing 3.3
Also according to PL website,
Lukaku has created 35 big chances in 220 games
Kane - 23 in 153 games
In general chances created, in last 2015-16 and 2016-17 season,
Lukaku created 97 chances in 6441 mis
Kane created 85 chances in 5906 mins
This season both players created 33 chances but Lukaku played 120 mins less.
Also both Kane and Lukaku were dispossessed 124 times. Kane 64 times due to unsuccessful touch, Lukaku 76 times.
Also regarding close control, Lukaku completed more dribbles with higher success rate in 2015-16 and 2016-17 season (haven't checked for 2017-18).
Kane is obviously better player but you are selling Lukaku way too short here. He is much better player than how you have described.