Under normal circumstances, the parking lot is private property, meaning that police do not have jurisdiction there regarding parking or traffic. In other words, you can't get a ticket in a parking lot. Unless the property owner has requested that the police patrol the lot and write tickets, and the police agree to do so, and are allowed to (or not disallowed) by local ordinance. That's going to be pretty rare, though.

In cases like yours, and OP's, the resolution is for the owner of the parking lot to have the vehicle(s) towed. At a standalone store, the store is not going to be eager to anger a customer by towing their car. At a strip mall, the operators of the stores probably do not also own the parking lot, and so wouldn't have the power to tow.