My Lightroom was freezing so I tried to update it using creative cloud app. When I clicked on update nothing happened.
After this I decided to uninstall Lightroom CC Classic and install it again. The uninstall process was fine but now, when I click on Install using Creative Cloud App, nothing happens again.
What is your operating system version number (I want the number and not words like "current" or "up-to-date")?
Lightroom Classic requires OSX Sierra or High Sierra. Maybe you are on an older operating system.
Update to the 10.13.4
It will fix the problem.