Yes, it’s very possible you could sue the shopping center for a crime that occurred in the parking lot. It would be necessary to look at certain things in the case to know for sure. Was there a dangerous situation that existed where the owner knew or should have known and did not take any action to make the location more safe? In this situation, we’re talking about crimes, or at least this one crime. The question would be whether crimes had been happening in this parking lot in the recent past where the owner knew and took no action. If it happened at night, was there sufficient lighting? If not, and they didn’t add more lighting, they could be negligent for that. If there was not enough security personnel, and they didn’t add more security personnel, they could be liable for that.
If there were no sufficient cameras after these crimes started occurring, that could be a factor to be considered in whether they were liable or negligent security. In addition to that, did they take any other actions or fail to take any other actions that could have made the location more secure? Did they put up warning signs? Did they have security guards patrolling as well as being inside the building? All these things would need to be considered. And if they were negligent by not doing things they should have, if they had information of dangers, or they took no action, they very well could be negligent.