Preheat your oven to 425°F (220°C).
In a large skillet, melt the butter over medium heat. Add the chopped onion and celery, cooking until softened, about 5 minutes.
Stir in the flour and cook for 1 minute, stirring constantly.
Gradually whisk in the seafood stock and heavy cream. Bring to a simmer, stirring frequently, until the mixture thickens, about 5-7 minutes.
Add the cooked lobster, peas and carrots, boiled potatoes, Old Bay seasoning, salt, black pepper, and paprika. Stir to combine and remove from heat.
Roll out one pie crust and fit it into a 9-inch pie dish. Pour the lobster filling into the crust.
Roll out the second pie crust and place it over the filling. Seal the edges by crimping with your fingers or a fork. Cut a few slits in the top crust to allow steam to escape.
Brush the top crust with the beaten egg for a golden finish.
Bake in the preheated oven for 25-30 minutes, or until the crust is golden brown and the filling is bubbly.
Let the pot pie cool for 10 minutes before serving.