It will depend upon the type of damage your vehicle sustained in the parking lot if it will be your comprehensive portion or collision portion of your physical damage coverage that will cover it.

If the car was hit by another vehicle or an object, such as a shopping car, then it would normally be your collision coverage that would cover the damage. You can make a claim with your insurance company and the claims adjuster should be able to make a definitive determination regarding which coverage the claim should go under. You will need to pay the deductible associated with that portion of your physical damage coverage for the car to then be repaired.