Place dough in a bowl and let it rest until it doubles in size, approximately 1 hour.
Preheat oven to 450°F with a pizza stone if using.
Punch down the dough and hand-stretch it into a circle, then place it on a well-floured pizza peel or pizza pan.
In a small bowl, combine minced garlic and olive oil, then spread the mixture over the dough.
In a medium bowl, combine cheeses. Sprinkle half of the cheese mixture over the dough.
Arrange lobster evenly over the cheese, then sprinkle with thyme and red pepper. Finally, sprinkle with the remaining cheeses.
Bake in the preheated oven for 20-25 minutes, until the crust and top of the pizza are golden brown.
Remove from oven and serve with lemon wedges for a refreshing finish. Enjoy your delicious lobster pizza!