I can't imagine a reason why it wouldn't be legal. A parking lot is not a roadway, so the only rules that apply to driving there should just be the basic right-of-way rules.
Regardless of whether it's officially legal or not, it's completely legal in the everyday sense of the word, meaning you'll never ever ever get in legal trouble for doing it. There are zillions of crazy laws on the books that aren't enforced that say things like you may not wash a goat in an apartment bathtub or other weirdness like that. If it's not an enforced law, then for all intents and purposes it's legal.