State laws differ so it would depend upon your state's specific laws if it is illegal for a minor to drive in a parking lot without a permit or license.
In general it is inadvisable for a minor or anyone to drive without a permit or obtaining driving privileges from your state licensing agency because accidents can even occur in a parking lot. We have heard from drivers that have had accidents with light poles, walls, curbs, etc in parking lots and if there is an unlicensed minor driving the vehicle then he or she likely would not be covered by the parent's or car owner's auto insurance for any incidents since he or she was not supposed to be operating a vehicle.
If you are asking if a teen or minor can be ticketed for driving in a parking lot without a permit, it would be up to state laws. Some state laws may only cite drivers that are operating without a license on a public roadway while others may be able to ticket an unlicensed driver no matter the location if they are found operating a car by a law enforcement officer.
Your state's Department of Motor Vehicle or local police station may be able to advise you of your state's laws regarding a minor driving without a license on private property, such as a parking lot. If it is illegal they should also be able to tell you what the penalties would be if the teen was caught and ticketed for this offense.