To update your billing information, first login to your Lycos Domains account.
After logging in, your username should appear in the top right of the page. Click it to expand a menu with several links:
Click on "Edit My Billing Info". From here, you can view the payment methods on file. To add a new credit card, click on the green "Create Credit Card" button near the bottom. You can also add a PayPal account from this screen too, with the green "Create PayPal" button.
If you have more than one payment method, you can switch your subscription services to use the new payment method. There will be another green button now, labelled "Switch Payment". Click on this leads to a screen where you can select which services you would like to change the payment method for.