Technically, yes. The parking lot is private property of the employer, or of the landlord of the employer. Either can prohibit you from carrying a firearm in your car. The question is, how will they know that you have a firearm in your car?

In Ohio your employment is "at will" and you can be terminated easily. If your employer asks to search your vehicle and you refuse, it could be reason for termination. If you allow them to do so and they find a firearm, they could terminate your employment. It is best to review your company policy and determine what the rules and regulations may be. Many companies already prohibit firearms anywhere on the property of the company, which is different in each unique scenario.