Lukaku had one good season in Italy (which is not anywhere near as good as it was before; see Italian clubs performance in both the CL and Europa) and Kane has pretty much outshone him every year while they both were in the Premier League. Apart from better goalscoring, Kane is much better on the ball, has an eye for a pass and had so many assists to Son last year. He's the real deal. As for Lukaku, the less we talk about his first touch the better. He's a striker than needs the whole team setup a certain way for him to be effective.
As for the record with the national team, Belgium is slightly better than England (at least over the last decade) and Lukaku has been pretty much the spear of an attack with Kevin De Bruyne, Hazard and Mertens feeding him balls, he should be scoring a ton.
I thought they are always among top 3 striker in the league back in PL time, remember at one point they are on race on who get their first 100 goals in PL. Of course I always rate Kane higher. But in recent years, I feel they have been getting at closer level
Club
12-13: Lukaku 17 goals vs Kane 0 goals
13-14: Lukaku 16 goals vs Kane 4 goals
14-15: Lukaku 20 goals vs Kane 31 goals
15-16: Lukaku 25 goals vs Kane 28 goals
16-17: Lukaku 26 goals vs Kane 35 goals
17-18: Lukaku 27 goals vs Kane 41 goals
18-19: Lukaku 15 goals vs Kane 24 goals
19-20: Lukaku 34 goals vs Kane 24 goals
20-21: Lukaku 30 goals vs Kane 31 goals
International
Lukaku 64 goals vs Kane 38 goals