According to Nolo, determining the right of way in a parking lot depends on the situation. If a car is backing out of a parking space and hits a car driving down the parking lane, the accident is the fault of the driver who is backing out.
Nolo points out that there are exceptions to every rule. Usually, it is the fault of the car backing out of a parking space if that car hits another. However, if the car coming down the parking lane was speeding, the liability is on the speeding driver. If a driver pulls forward in a parking space and hits another car trying to park, it is the fault of the driver pulling forward.