Probably not unless you can prove that the business owner or the company that owns the lot that serves the business clearly violated state laws and city ordinances regarding the design and maintenance of the lot. A business or lot owner cannot be held responsible for the actions of a negligent, reckless or inattentive driver, but an injured pedestrian might have a claim against a business or lot owner that allowed the condition of the pavement to deteriorate to the point that the lot was not safe for anyone.
Clearly unsafe parking lots would be those that lack required lighting, those covered with uncleared snow and ice, and those without marked crosswalks. A lot with massive potholes could also be considered unsafe enough to make a business or lot owner subject to what Virginia personal injury lawyers like my colleagues and I call a premises liability lawsuit.
EJL