Downvoted. I'm Italian. Nevertheless. De gustibus non disputandum est. But quality ingredients and culture make all the difference. Fun fact: I eat pasta once a month and pizza twice a year. Yet Italian and Spanish ingredients beat ingredients/produce from any other other European country.
This is kinda funny, and I know the concept of "authentic" isn't particularly easy to nail down, but my experience is that Italian lasagna doesn't have tomato sauce. It's always been thin pasta, a ragu, and bechamel. It generally changes to match the tastes and ingredients of where it's being made, but maybe you'd like the version I know.
I had moussaka in Greece a few years ago and liked it too!
Ragu is a general term for meat sauces some of which have tomatoes but not all. The recipe I use I wouldn't call a "tomato sauce" but it has tomatoes. In the US most ragus are much more tomato forward if that's your frame of reference.