My creative cloud is showing Lightroom classic as installed but I cannot get it to open

Yes there seems to be a problem for some users but as Johann said, we need more information. First thing is if you have Windows, check to see if it's running in the background, if you know how to do that.

You need to give more information. Your hardware specs, your OS (Mac or Windows) with version number. And what exactly happens when you try to launch Lightroom Classic.