Would you restart an engine that has been shutdown due fire? How bad is your day that you would have to consider this as an option. The premise of ETOPS is that statistically the second engine will not have an occurrence that results in loss of thrust, therefore this consideration should not be required. However the Air Transat A330 incident shows that when humans are involved statistics do not acount for everything.
Oil supply is required for lubrication as the fan and core will 'windmill' from the airflow.