Add 4 cups of salted water to a large pot and bring to a boil. Add the fettuccine and cook according to the package directions until al dente. Drain and rinse under cold water. Then return the pasta to the pot and toss it with 2 tbsp butter. Set aside.
Preheat a deep-sided skillet over medium-low heat. Add 4 tablespoons of butter to the pan. Once melted, add the minced garlic and onion and place the lobster tails on top.
Pour the lemon juice and wine into the skillet. Then cover the pan and cook for 7 minutes.
Remove the lobster from the pan and place them onto a wooden cutting board. Let the lobster cool for 5 minutes, then remove the meat from the shell. (see note)
Add 2 tablespoons of butter to the skillet and increase the heat to medium. Slowly add 1/4 cup of half-and-half at a time, whisking as you go. Once fully incorporated, whisk in the salt, pepper, Old Bay, Parmesan, and mozzarella. Cook for 7 minutes.
Chop the lobster meat into 1/2-inch pieces. Add the lobster and fettuccine to the sauce and stir until coated.
Garnish with chopped parsley and a sprinkle of Old Bay before serving warm.
Notes
If you don't have salted butter, you can use unsalted butter and increase the salt to 1 1/4 teaspoons.Here's a video on how to remove the lobster meat from the tail: https://www.youtube.com/watch?v=2vVH5eMnnEM