Cook the lobster shells with garlic in a small amount of butter over medium heat until fragrant, about 2 minutes. Add water to cover and simmer for 20 minutes, then strain to make a rich lobster stock. Set aside.
Mix the flour and eggs together in a bowl, then knead into a smooth, elastic dough. Wrap in plastic and let rest for 20 minutes to relax the gluten.
Divide the rested dough into small portions and roll out thinly using a pasta roller or rolling pin, dusting with flour to prevent sticking. Aim for sheets that are almost translucent.
Cut the rolled dough into 3-inch squares using a sharp knife or cutter. Keep covered with a damp towel to prevent drying out.
Fill each square with a small spoonful of finely chopped lobster meat mixed with lemon zest, tarragon, salt, and pepper. Brush edges with water, then fold over and press to seal, ensuring no air pockets remain.
Bring a large pot of salted water to a gentle boil. Carefully drop in the ravioli and cook for 3–4 minutes, until they float and are tender.
Meanwhile, melt butter in a saute pan over medium heat. Add lobster shells and cook for 2 minutes until fragrant.
Add lobster stock to the shells and simmer for 10 minutes, then strain to remove shells, leaving a flavorful broth. Reduce this broth slightly until it thickens a bit.
Stir in the heavy cream and lemon zest into the reduced stock, simmering gently until the sauce thickens and becomes velvety, about 5 minutes.
Using a slotted spoon, transfer the cooked ravioli into the sauce, gently tossing to coat each piece and letting them soak up the flavors for about a minute.
Serve the lobster ravioli hot, garnished with extra tarragon or lemon zest if desired, and enjoy this elegant yet approachable seafood dish.
