I think the term is used differently in different regions. Italy has so many micro-cultures lumped together, each with a very unique food heritage. When I lived in Venezia (Venice), no one used the term lasagne, it simply wasn't a dish they made. But they all made Pasticcio, a regional favorite with local varieties of radicchio or artichokes with besciamella. The noodles were not varieties of pasta shapes, they were the classic flat sheets.
Slightly off-topic but fun story: We had a friend from another region of Italy (where Lasagna is prevalent) and got onto the subject of Italian and American Lasagne, and they scoffed at our version, mocking it by saying that it was probably made with ketchup and tasting bad. I challenged them, that we should all make our own versions of lasagne- the American, the Italian and the Venetian (Pasticcio), and we did. And all were duly impressed with the American version :)
So, at the end of the day, I don't think there is one Italy, there are hundreds of local traditions with variations that can change within 10 kilometers from town to town.
Tip: When I am looking for authentic versions, I always trust the Italian language recipes, not the english versions. With google translate now you can easily read authentic local recipes! Try googling "Pasticchio Carciofi" vs. "Artichoke lasagne". The difference is huge. You can search for regional names too, like "Pasticchio Veneto" to get acquainted with regional varieties.