Dale has the right answer, but I'd like to elaborate on why it isn't lawful (as compared to why it would be unlawful).
I know it doesn't work that way on line, but it's simpler to think of a credit card as a physical piece of plastic. The bank will have issued this to their customer. It will have a number and an expiry date. You have no way of knowing whether a replacement card has been issued. Even if one has, the customer has authorised you to charge a specific card - you do not have the customer's authorisation to charge a different card with a different expiry date.
By guessing the expiry date, you would be making a representation to the bank that the customer has authorised you to charge that card (if it exists), when they have not.