If you used paypal subscription then the billing will be automatic. If you are using invoice, then the billing system will send you invoice each month.
I think you can register for more than a month , just contact the billing department and ask them for making a new invoice for you. They will sure , help you.
Once you installed the litespeed with the NEWLY created serial number, its done. You dont need to reinstall or change the serial number every month. It will automatically get renewed when you pay the invoice.
I hope this helps you.