Preheat oven to 400 degrees F (200 degrees C). Butter 2 gratin dishes.
Heat oil in a skillet over high heat. Cook lobster tails in skillet until slightly golden and about halfway cooked-through, about 2 minutes per side. Transfer tails to a plate to rest. When cool enough to handle, remove lobster meat from shells and chop meat. Reserve shells.
Melt 2 tablespoons butter in the same skillet over medium heat. Whisk in flour; cook and stir until a paste forms and flour taste cooks off, 1 to 2 minutes. Add cold milk to flour mixture; whisk until completely incorporated. Bring to a simmer; reduce heat to low, and stir in paprika, nutmeg, and cayenne pepper. Cook, stirring occasionally, until thick, 3 to 4 minutes. Season sauce with salt.
Stir Cheddar cheese and Gruyere cheese into milk mixture until cheese is melted. Remove from heat and stir Worcestershire sauce into cheese sauce.
Bring a large pot of water with reserved lobster tails and a pinch of salt to a boil. Cook elbow macaroni in the boiling water, stirring occasionally, until cooked through but firm to the bite, about 8 minutes. Remove and discard lobster shells, drain pasta.
Stir macaroni into cheese sauce with thyme leaves. Divide macaroni mixture between the 2 prepared gratin dishes. Top macaroni with chopped lobster meat, poking meat down into macaroni mixture with a fork.
Stir bread crumbs and melted butter together in a bowl. Add Parmesan cheese and stir. Top each gratin dish with bread crumb mixture.
Bake in the preheated oven until golden and bubbly, 15 to 20 minutes.
Make sure your mac and cheese mixture is wet and saucy in the pan, otherwise it might get dry when it bakes. Don’t be afraid to add a splash of the pasta water to loosen things up.
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