I was attacked in a shopping mall parking lot. Can I sue the owners for my bills?

Generally, the owners of a business are responsible for reasonable security on their property. Reasonable security would include adequate lighting and security staff, among other measures. Also, if other crimes were committed, this would demonstrate a pattern of criminal activity that the owner would have been aware of – and should have provided additional security to counteract. You should gather any documentation, including police reports, details of medical care resulting from your attack and any other expenses, and contact a premises liability attorney who can advise you whether your situation merits legal action.