Photoshop Lightroom isn't available to install from the Creative Cloud desktop app when you are logged in with a free membership account.

Solution

Download the trial version of Adobe Photoshop Lightroom from the Lightroom product page on Adobe.com.

After you have purchased a Creative Cloud individual, team, or enterprise membership, Lightroom is available for installation within the Creative Cloud desktop app. If you have already installed the trial version of Lightroom, you can license it by running the Lightroom installer from the Creative Cloud desktop app.