Heat a grill to for medium high indirect heat. Grill the sausages for 3 to 4 on each side. Set aside to cool while you mix up ricotta filling.
Whisk up the egg in medium mixing bowl. Add the ricotta, Pecorino, Parmesan, garlic, and basil. Thinly slice and roughly chop the sausages.
Be sure to use a heavy bottom ceramic maxing dish for the grill. Coat the bottom of the baking dish with a couple spoonfuls of red sauce. Layer on two of the lasagna sheets, followed by the ricotta filling, some of sausage, and a handful mozzarella. Repeat for with two more layers and a final layer of lasagna sheets and cheese.
Cook the lasagna on grill for 30 to 40 minutes until totally bubbly and golden brown. Let the lasagna cool for 10 minutes before slicing.