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.