If your leased car is damaged but can be repaired, you will need to keep paying your monthly payments until the car is fixed and drivable. Whether repairs are covered will depend on the terms of your insurance policy.
You may be required to receive repairs only from recognized or authorized professional body shops, or a repair shop for that specific car brand. Repair work may need to be done in a way that restores the leased car like new, using only original manufactured parts and not after-market or off brand parts.