Welcome to Adobe Forum,
Do you have beta(trial version) installed for light room? If yes, then uninstall it completely by checking the preference boxes too.
Now restart the computer & download & install from the CC desktop App. It should work.
In case it does not work, contact Adobe support at http://adobe.ly/yxj0t6.
Please Sign out and then Sign in to CC App Manager.
You may also refer to the below mentioned link under first and second option:
Let us know if it helps,
I search the community for the other supports and found advice to delet a file from Library/Application support/Adobe/... and sign in. I did and it worked.