The right to defend yourself ( be armed ) in your PRIVATE vehicle would IMHO trump a ban on the parking lot where you work . Unless you work in a school where the law stipulates no firearms within a given distance of the school grounds .
Understandably, this has always a point of contention.
I carrry concealed, either on my person or in my car, in Indiana daily. The subject of weaponry in private vehicles on other people's property is a tough nut to crack, indeed.
However, If your weapon is in a vehicle and it's on my property, your weapon is on my property. As the property owner, I should have sole discretion as to how my property is used. If I start letting The State determine the rules of use for my property, they will ultimately claim that property.