Heat grill over medium-high heat. Cut the top of the lobster tail shell using kitchen shears, leaving the fin intact. Brush the meat with olive oil. Grill belly side down with the grill closed for about five minutes. Flip and cook until the lobster is opaque, about another five to seven minutes.
Once cool enough to handle, remove meat from shells and wrap in foil or place in a 200-degree oven to keep warm.
As the lobster tails cook, began boiling water for the fettuccine. When you start the sauce, you can start cooking the fettuccine. Once the fettuccine finishes cooking, reserve some of the pasta water.
Melt butter in a saucepan over medium heat. Add heavy cream and stir to combine. Bring to a low simmer but don't let boil.
Stir in garlic, salt, nutmeg, grated Parmesan and Romano cheeses, and cream cheese. Stir constantly until melted. Again, don't let boil. Turn down the temperature if need be.
In a separate bowl, scoop a ladle of sauce with the egg yolk and stir. Do this a few times to ensure the egg mixture is warm before going into the rest of the sauce. Then, add the egg yolk mixture back to the sauce. Simmer over medium low heat for 3 to 5 minutes. Stir in lemon zest and lemon juice. If you need to thin out the sauce, add a little reserved pasta water until it reaches your desired consistency. You can skip this step if you're good with the thickness. Turn off heat.
Directly in the saucepan, stir in fettuccine and lobster. Divide among bowls and garnish with additional grated Parmesan cheese, fresh parsley and lemon zest. Enjoy!