And the lot in which you park your car is the property of the owner, and you are parking there under his permission, so he has the right to set the rules as to what you bring in--and the conditions of doing so.
There are certain legal limits to the restrictions one may impose when one openly invites the public onto one's property.
If the parking lot had a fence and a manned gate with a prominent "Defenseless Victim Zone" sign posted along with all the other conditions of entry onto the property, perhaps including physical search, they might have some wiggle room on this, but an open parking lot with multiple entrances and no access control is another story, and that represents the vast majority of businesses across the state.
And aside from that, a corporation is a creation of the State, so while in some respects it retains the rights of its pseudo-person status, it is entirely subject, as a creation and privilege of government action, to the regulatory action of the government.
And besides, is the gun-banning business willing to be strictly liable if someone they've "contractually" disarmed is harmed by a violent criminal to, from, or while at their place of business? If a battered wife is brutally assaulted by her infuriated ex-husband (who also has access to the unguarded parking lot) while getting out of her car on her way to her cubicle, will that business pay the full sum of her medical bills and lost pay?
If they didn't wash their hands of the obvious consequences of disarming lawfully armed individuals, there wouldn't be such public and legislative outrage about this situation.
More concisely - I’ve seen this discussion framed as a “right to a safe workplace” by banning guns. But that’s almost Orwellian - the only safety that banning the guns of licensed, background-checked law-abiding citizens insures is the safety of a violent attacker.