Unfortunately stop signs in parking lots are not the same as stop signs on the street when it comes to determining fault. Parking lot accidents are often difficult to assign fault
for insurance companies so they may ultimately decide to cover only their own customer's damage by saying the that fault was 50/50 between the drivers. I would recommend contacting the other driver's insurance company to see if they will cover your damage based on the information you provided. If they decide not to then you will have to contact your company for repairs.