Agallia I have not tested that scenario but it is likely your perpetual license will continue to be utilized. If you wish to free up your perpetual license for installation on another computer then I would recommend removing your current installation of Photoshop Lightroom and reinstalling through the Creative Cloud Desktop application.
You can find more details on how to uninstall and reinstall at Install and update apps - https://helpx.adobe.com/creative-cloud/help/install-apps.html.