Adding eggs to lasagna
The version of lasagna that I grew up making was a collection of layers of various things. These layers were (at minimum) - sauce; pasta noodles; a mixture of white, soft cheese and other things; and other cheeses, usually mozzarella. This means that there are actually two cheese layers - one shredded, the other creamy. Here's a recipe I've grabbed from Food Network as an example.

One of the steps involves combining the ricotta (some people use cottage cheese instead) with other ingredients including the raw eggs:


  In a small bowl, combine the ricotta, 1/2 the Parmigiano-Reggiano, the eggs, and the basil. Mix to combine well and season with salt.


This mixture is then layered, alternating with the noodles, meat, vegetables, and sauce. The other half of the Parmigiano is sprinkled on top with mozzarella for the cheesy topping and a bite of saltiness. I'm reformatting the quote below to show the different layers more obviously.


  In the bottom of a 9 by 13-inch deep-dish baking dish:  
  
  
  add a couple ladlefuls of sauce and spread out in an even layer. 
  Arrange a layer of the lasagna noodles to completely cover the sauce.
  Spread 1/3 of the ricotta mixture over the pasta. 
  Place a layer of pasta going in the other direction as the first layer (this will give a little more stability).  
  Spread a light layer of sauce on the pasta and sprinkle 1/3 of the sausage over the sauce, 
  [Spread a light layer of sauce on the sausage and sprinkle] 1/3 of the mushrooms and zucchini. 
  Sprinkle a layer of mozzarella and some of the remaining Parmigiano-Reggiano over the veggies. 
  
  
  Repeat these layers until all the ingredients have been used up or the pan is full. Be sure that there is a layer of pasta on top covered with sauce and sprinkled with mozzarella and Parmigiano. Cover with foil.


So, to answer your question, yes, the egg is mixed in, raw, with the cheeses to make the cheese layer... but if you're not using a ricotta or cottage cheese and are just using shredded cheese, you probably shouldn't do this.