Using Little's law to find the average N of customers
Your intuition was right.  As you hinted, Little's law only applies to a stable system.  This is not a stable system.  The arrival rate exceeds the rate at which customers can be serviced.  Therefore, the number of customers waiting in line will grow without bound, getting increasingly larger as time increases.  That means this is not a stable system.

You can only apply Little's law to stable systems.  Since this isn't a stable system, Little's law doesn't apply.