There are two LR’s, the standalone one that uses a serial number for licensing and the CC one that uses a CC login for licensing.
If you purchased the Photographers Program for $9.99/month or some other CC option that includes LR, then you have a license for the CC version. However, only one LR can be installed at a time and since the non-CC version is installed CC won’t offer its version for install.
What you should do is uninstall the standalone serial number LR, and reboot or at least restart the CC Cloud App, which will tell it to rescan what is installed locally and see that LR is no longer installed, and offer it in the CC Apps list with an Install button next to it. Click that..
The CC version of LR will pick up where the non-CC version left off so your catalog and preferences and photos will be the same as before.