I imagine if at the time the 2nd Amendment was written, someone had mentioned a parking lot, the writers would have asked "What in the hell is a parking lot?" Sure, but they'd have known what a livery stable or hitching post was. Then the question would be could an employer prohibit someone from having a horse pistol on their saddle if the horse was tied up, or corralled, on the property of the business.
It is my understanding that saloons would often prohibit guns on the premises, and in some cases sheriffs would do the same for the whole town.