If I opened an a credit card in California can the lender change the terms and conditions if I move to Kentucky?

No.

Most credit card lenders do what is known as "Exporting" terms and conditions. In this case, no matter where the card is issued or carried, the terms and conditions apply.

If you move to Kentucky, be sure to let the card company know your new address and contact information so they are up-to-date and can reach you if they detect faudulent activity.