Yes, they can ban a gun in a car even in the parking lot.
In TN you can not even have a loaded weapon in your car unless you have a permit. So TN does not treat your car as an extension of your home like some other states do.
T.C.A. 39-17-1359 says a property owner can ban firearms anywhere on their property.
So if the employer does not have a sign posted and has only stated, either verbally or in an employee handbook, that weapons are not allowed, then you would not be breaking the law by having on in your car,just company policy. So it is likely you would be fired if they found out and/or you refused to allow your vehicle to be searched.
Thereare a couple ofbills HB1395 and HB1793that has been sent to summer study that would allow employees to keep a handgun locked in their vehicle on company property.