After today, I've resigned myself to the fact that he'll never ever truly be elite (in the eyes of the World, however much value you want to assign to that).
Immobile is perhaps one of the greatest 20 or 30 forwards in Serie A history, but no one outside Serie A gives a shit about him. What with the World Cup (however fair you think that is judging him upon, seeing as he had an injury apparently) and his showings when it really mattered in Europe, this is what Lautaro will be perceived as. 12 goals in 44 Champions League matches ain't it, dog. Milito was it, Lautaro won't be.
I don't see that changing, even though he's taken strides in Serie A. Goals against Cagliari and whoever won't get you recognition, but skying that penalty will get you plenty of attention on Reddit and on replays for years to come. That's how non-Inter fans will perceive him, not scoring against Milan in a semi-final (that was already decided) - it's a fickle world, but that's how it is.
He's still great for us and we can't get better, mind you.