Throwing a kid to the wolves and overwhelming them is more on dad, as to many think little Jr can really wheel his little quad or back yard kart so let's go racing, They go buy good stuff and all they basically tell the kid is go show them how it's done, at a race they have no business at in the first place.
Personally for me to even consider a parking lot it would have to be wide open area NOT a single vehicle in it and NO other obstacles, and I had permission from the owner ( which will be tough in today's world ) remember Murphy's law applies in all cases of karting, so I would have a kill switch for the motor up on the wheel, then go over EVERY possible scenario that may happen, of course have and use all safety equipment.
Even if you find that I would still find the closest track to me and work out the best deal I could with the track owner, to get maximum amount of laps possible per trip, even If they have NO practice races start out season racing points .I would talk to them and not enter per class I would ask to be by himself most will squeeze it in, and If they allow track time after races take advantage of that. Then once you get him in with the others based on what your seeing with him and his class, don't pressure him to run up front and request he start in the rear, IF you set a goal make it reasonable again based on what your seeing it may be only get lapped twice, or once, or just stay on lead lap, while this is going on be patient and you learn as much about set-up, tires, prep as possible. Go over all the flags and hand signals with him, when he's not out have him at the fence watching was much as possible, at 9 yrs old he should pick it up little quicker but you never know.
For his first race with other experienced kids prepare him once they catch him to lap him what to do, make sure he knows how many in his class when they start lapping him move up to high side of the groove let them go, but don't panic stay sooth, make sure how many there are don't as soon as one goes by cut right back down in groove because there will be more coming. Make sure you get a good base line under it as long as it's handling leave your fingers off of it for awhile not trying to fins speed UNTIL the driver is ready to find speed, I've seen dad's spend thousands more to try to run up front when what there on will run up front, the only reason there not is the kids not ready to. Make it FUN !!
Good Luck !!