Preheat your oven to 350°F (175°C).
Cook the elbow macaroni according to package instructions; drain and set aside.
In a saucepan, melt butter over medium heat.
Add flour to the melted butter, whisking continuously for about 2 minutes.
Gradually add milk, whisking until the mixture thickens.
Stir in cream cheese until melted and smooth.
Add cheddar and Gruyère cheese, mixing until fully melted.
Combine the cooked pasta and chopped lobster with the cheese sauce.
Transfer to a greased baking dish and bake for 20 minutes or until bubbly.