Hi Kelly,
There is no Last Invoice Date field on the stock Customer and Contacts List screen. Are you perhaps referring to the Last Activity and Next Activity fields? If so, these fields are special Method fields and cannot be modified in any way.
If you do see a Last Invoice Date field on your screen, then it was created via customization. There are a couple of ways that we would normally use to populate such a field. The first is via an SQL override and the second would be to run an action set that would loop through your customers, retrieve the most recent invoice date and store it in a custom field on the customer table. The logic of each can be changed by modifying your SQL override query or your action set respectively.
I hope this helps.
-Audisho