Preheat oven to 375 degrees F.
To a medium pot, set over medium heat, add the butter. When the butter has melted, add the flour and mix it together and cook the flour butter mixture for about 1 minute. Pour in the milk in two batches, stirring continuously in between additions. Cook until it thickens up, about 2 to 3 minutes. It’ll start to bubble up and thicken. Give it a good whisk and be sure to get in those corners of the pan to get any floury bits up and mixed in. It should be thick enough to coat the back of a spoon.
Turn off the heat and whisk in the kosher salt, crushed red pepper, Dijon mustard and a few rounds of pepper. Give it a taste and adjust the salt to taste. Add the grated cheeses and mix them in until they’re melted. Cover the pot with a lid and set aside.
Meanwhile, bring a pot of salted water to a boil. Cook the pasta according to the package’s instructions, about 9 minutes.
Drain the pasta and then immediately add it to the pot with the cheesy sauce, along with the reserved lobster. Mix until thoroughly combined.
Transfer to a 9 x 11-inch baking dish (or one that is comparable). Smooth it into an even layer and then top it with the reserved breadcrumbs.
Transfer it to the oven to bake for about 15 to 20 minutes, until the top is lightly golden brown.