If you are driving your personal car on a business errand and your car is hit in the parking lot who is responsible for the damage you or the company?

Your insurance company may deny the claim due to business use, but they would be the primary coverage. Insurance stays with the car. But your employer should certainly offer to pay for this damage. I would file with my company and if there is coverage, maybe your employer would pay your deductible, if it is denied then file with your employer. If you would like to provide more details I could be of greater assistance.