Lorina Pro is not available from wordpress.org like the free version is, so you will not see it by searching for new themes in your site’s dashboard.
You should download the theme from the link in your payment confirmation email, or from your account here on our website.
Save the theme to your computer and then in your site dashboard, go to Appearance > Themes, click the ‘Add New’ button, then the ‘Upload’ button and then ‘Browse’ to find the lorina-pro.zip file that you previously saved to your computer, and then click the ‘Install Now’ button.
There is no activation key. The theme will just work when you install and activate it.
There is a license key that you can optionally enter after installing the theme. It will work without the license key, but to get automatic theme updates in your dashboard you would need to enter your license key.