Melt the butter in large saucepan over medium-high heat. Whisk in the flour and cook for 1 minute. Add the hot stock, milk, and cream and whisk until the sauce begins to thicken. Cook for 5 minutes, whisking occasionally.
Remove from the heat and whisk in the cheeses and season with salt and pepper. Add the parsley, thyme, tarragon, and pasta and stir until combined. Chop the lobster into bite-sized pieces and fold into the pasta. Divide into bowls.
For the crumb topping: Preheat the oven to 350 degrees F. Spread the breadcrumbs on a sheet pan and toast until barely golden, stirring once or twice, about 10 minutes. Heat the olive oil in a medium skillet over medium heat. Add the anchovies and stir a minute or 2 to warm through. Add the breadcrumbs, season with salt and pepper, and cook, tossing, until warm and slightly crisp. Remove from the heat and stir in the parsley and lemon zest. Sprinkle generously over the pasta.
Heat the oil in a large stockpot over medium heat. Add the shallots and cook until soft. Add the wine, bring to a boil, add the mussels, cover and cook until the mussels have opened. Remove the mussels to a bowl for another use, and then strain the broth into a saucepan.