In a medium saucepan, melt butter and add flour 1 tbsp at a time, whisking until flour is dissolved into the butter.
Cook roux for 2 minutes, until a light blond color.
To the roux, slowly add milk, whisking constantly.
Once the milk is added, add in heavy cream, slowly while simultaneously whisking the sauce. You do this so that you don't have any lumps in your béchamel sauce.
Once heavy cream is added, allow the sauce to thicken, continue to stir.
After about 3 minutes, the sauce should begin to thicken. At this point, lower your heat, and add your cheese a handful at a time, allowing each handful to melt into the sauce.
After you've added about a cup and a half of cheese to the sauce, add in your seasoning. Taste the sauce for saltiness and adjust as needed.
Turn off the heat on the sauce and add in your chopped lobster meat and stir.