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Going with no, at least if you require the “pasta” to be the same thing for both, ingredients wise.
Please notice how the spaghetti have no egg (uovo) in the ingredients, as opposed to the lasagna.
You know that both of them have "with eggs" and "no eggs" varieties, right?
You can also make a cake without eggs.
I will unfriend and block you, but it’s possible.
If you are talking about Lasagne - the pasta type and not the finished product, you would be right in saying you can find it both with eggs and without, by the article it says it is a north/south thing in Italy. But honestly you can find thousands of variations of them even moving just a few dozens kilometer.
On the contrary to be spaghetti and not something else they need to be - to directly quote - "a special pasta format made exclusively from durum wheat semolina and water, with a long, thin shape and round cross section."
I'm not sure if it is the same outside of Italy. But at the end just do what makes you happy.
Fair, but neither is the regular kind. Generally speaking, lasagna, tagliatelle: eggs. Spaghetti, fusilli, penne and so on: no eggs.
Edit: actually, might be worth pointing out that this is in Italy. It’s true that recipes can change wildly in different countries…