when you launch Lightroom and you receive the prompt of trial, there would be another option "License this software" which you need to choose and enter your serial key to license it.
you can find your serial key under your account by going to this link : Adobe ID
I did type in my serial number but now I see above my name that is have 30 days left. Do I have to uninstall and do it again?
30 days trial message that you see under your Identity Plate in Lightroom is regarding the Lightroom Mobile trial.
Lightroom Mobile App is included only in Creative Cloud subscription package and not the standalone version and due to that reason it says trial for you.
You can turn off that message by choosing Pause next to the Mobile Sync under your Identity Plate dropdown menu.
Thank you so much Chetna. I was about to give up.