Boil the 2 lobster tails in well-salted water over high heat for 5 to 6 minutes until the shells are red and the meat is opaque, then cool, remove the meat, and chop into 1-inch pieces.

Melt the 3 tbsp butter over medium heat, add the 4 cloves minced garlic and cook for 1 minute, whisk in the 1 tbsp flour for 30 seconds, then pour in the 3/4 cup heavy cream and simmer on medium-low for 3 to 4 minutes. Stir in 1/4 cup of the Parmesan, the 1/2 tsp salt, 1/4 tsp black pepper, and 1/4 tsp red pepper flakes, then remove from heat.

Preheat the oven to 450°F (230°C) with a baking sheet or stone inside, then stretch the 1 lb dough to a 12-inch oval about 1/4 inch thick and brush the outer border with the 2 tbsp olive oil.

Spread the cream sauce over the dough, top with 1 1/4 cups mozzarella, arrange the lobster pieces on top, then finish with the remaining 1/4 cup mozzarella and 1/4 cup Parmesan.

Bake at 450°F (230°C) for 10 to 12 minutes until the cheese is bubbling and the crust is deep golden brown, then scatter the 2 tbsp chives and 1 tsp lemon zest over the top, slice, and serve immediately.