If my disabled vehicle was parked in a parking lot and was then destroyed in an arson, is the owner of lot liable?

On what grounds would you sue? Do you believe the landlord or his staff burned the car? Or did the landlord make some representation (or promise or assertion) that cars were secure or that the landlord took responsibility for them?

If the above were true you may have a cause of action; if not, however, you very likely do not. The fact that a car is damaged or destroyed on someone's property does *not* by itself make someone owning or renting that property liable, or financially responsible. Instead, there must be fault, which is either an intentional act, a careless act doing the damage, or a careless or intentional failure to fulfill a duty to guard the property in the person's control--but simply parking on someone's lot does not impose on them such a duty. So unless the landlord did something wrong or promised in some way to take care of the car, he, she, or it is likely not liable.