Unfortunately most of us do not have part 107 and have zero interesting in making business connections, providing footage to anyone, or revealing our identifies to anyone.You might simply ask the owner/manager of the parking lot if they would allow you to fly from their private lot. You might even offer to provide them an aerial shot of the parking lot for letting you fly there. Sometimes the simplest answer is asking the simplest question from the right person, the owner/manager of the property. Never know it might even make you a connection that drums up some future business.
This answer does not rely to anyone in particular: I understand the rationale in asking and I believe there are some friendly flyers who live in friendly places where it makes sense to reach out to others and ask permission whether it is required or not. However, my only simple objection is it creates an unrealistic expectation that a drone flyer could/should/must/might ask before they fly and while this may be true for commercial flyers who are professionals who like to conduct business in a "respectable" manner consistent with their trade, it doesn't always apply to the recreational drone pilot who spots an interesting photo opportunity or the fpv flyer who catches a glimpse of an abandoned building. Doesn't really make sense to seek out the owner, have the discussion, exchange details, etc. This type of flyer is easy to say NO to, whomever you ask will likely tell you they don't have the capability to grant you the permission, etc. This type of flyer is spontaneous and will just fly for a few minutes, get their shot, and you're gone with a focus on don't bother anyone, do hurt anyone, don't climb any fences or open any gates, don't destroy any property, obey the signs, obey the police if they show up, leave it exactly like you found it....and no hard feelings. Who can say no to that?