You can store your lemon cobbler in the fridge for up to a week. Due to the lemon filling, it is best to be stored in the refrigerator to prevent spoiling. If you don't plan to eat right away, you can also freeze the cobbler. Do this by placing the cobbler in a freezer container or cover the pan it's baked in tightly in plastic wrap and foil. Freeze for up to 1 month. You can allow it to thaw in the fridge overnight and reheat it in a 350 degree F oven to firm up the topping if needed.