I normally prefer to avoid anyplace that tries to prohibit my ability to protect myself. So I'd likely not be there in the first place.
BUT.....As far as the parking lot goes, the sign says nothing against carrying in their lot unless they have it posted right on the edge of the property line--"No Weapons Beyond this Point". It's a wide open field as to whether or not they could even try to push something against you in their lot. In the event you had to draw in their lot, they'd likely become your best friend to keep you from suing them over the whole matter. "I come here to shop, not to get robbed/assulted/car-jacked. Is that your idea of safety for your customers? Good thing I can defend myself, because you are completely incapable of providing safety for me".
If a situation arose within the store I'd do nothing different than I would anywhere else. It's their responsibility to provide a safe environment within their store. I think I can handle my personal safety a little better than a 16-year old check-out girl armed with a laser scanner and plastic bags, should a (heaven forbid) life threatening situation ever occure. My personal safety is my responsibility. And if it does happen that I'm forced to draw, that point is made even more clear.
"Why is is called Common Sense when it seems so few actually possess it?"
Guns only have two enemies: Rust and Politicians.