1995 Buick Century oil light comes on and engine runs rough

Hello. Could use some advice on my daughters 95 buick century. Her cars oil light will come on after driving around town 20 min or so. Immed after the light comes on the car starts to run rough then check engine light comes on and it soon stalls. Usually about 1 hour later it starts back up and runs for an un predictable amount of time. Oil changes are current and not losing any oil or coolant. Car runs good till this happens. Like I mentioned, if it dies on its own It will not start for awhile, almost like it something needs to cool down.