Here are the details from each vendor:
Westlaw: Westlaw is allowing graduates to extend their password access to Westlaw databases until November 2013. If you have already extended your WestlawNext access, you don’t have to do anything further. Go here to extend your Westlaw Password.
Lexis Advance: Lexis is allowing graduates to extend their access to Lexis Advance through December 31, 2013. Apply here to receive a special Lexis Advance ID through a new Graduate Program. You will receive a new ID in early July that may be used for “for educational, bar preparation, and job search purposes only.”