I will assume that the light fixture was part of the garage.
There are a couple of theories worth examining. First, is this a bailment situation in which you transfer possession, but not ownership of your chattel? The courts tend to look at whether you park it yourself, who holds the keys, whether the lot is enclosed, etc..
In this situation, ther probably is not a bailment created.
Next, is there recovery under a negligence theory? The parking lot is a business
and the car owner is a customer. There is a duty of care owed to the customer or invitee to inspect and repair hazards on the property where your customers are.
Therefore, the fact that the owner had a duty to inspect the light fixture and repair it would indicate to me that the parking lot is liable for the damage.
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