www.mangiabedda.com/sicilian-lasagna/
There's a typical Sicilian lasagne recipe. It's also common to use boiled eggs in some northern Puglian provinces and parts of Calabria.
It's a bit ironic that people who would put anything in their fridge into a lasagne (I remember a very funny MNer talking about the Mumsnet Lasagne containing anything and everything - an old sock, half a tub of strawberry yoghurt, some roadkill etc etc) refuse to believe what Italians actually put in theirs.
I've only ever eaten it with boiled eggs once, and no, I don't want to it again.
My SIL's is made with no tomato sauce or cheese, and only artichokes and bechamel between the layers. Another SIL's contains no bechamel but only tomato sauce/Ragu. When we buy a takeaway one it tends to have chopped ham in it as well.
Where I am (Puglia, but not the boiled egg bit) mozzarella goes in with the bechamel. Makes it stand up better to be sliced.
As a pp says, recipes don't have to be prescriptive, not even for Italians themselves. But the base recipe remains meat sauce, bechamel, pasta. Soffritto of onion, celery, carrot to flavour but is invisible to the eye as it's chopped so finely.