You don't need to pay to renew your license if you just want to continue using the same version of the software that you already have.

In newer plugins, the last day of the free update period is shown in Lightroom's Plugin Manager for Lightroom plugins. When you use the "Check for Updates" function, you will be told whether the software was released after this date or not.

Older plugins will not be able to show this information, but you can check in the Helpdesk what the exact details of your license are. To do this, log into the helpdesk and visit the Licenses section.