I have passed my CCIE lab on June 6, 2006.
I wonder if there is any problem if I attended the prometric exam for one of the CCIE written just one week after expiry date of my lab certificate.
AFAIK, there is no problem.
As I understand it, from two years after your lab exam, your CCIE is still valid but dormant. That is, you are not allowed to quote it during the period between 6th June 2008 and when you pass the written. But you can still reactiviate it by passing the written, as long as you pass the written by 6th June 2009.
You can find chapter and verse on www.cisco.com/go/ccie - check it out.