The first thing I would suggest is to make sure that it comes from Link Library. Have you tried quickly deactivating the plugin to see if the problem still happens, then reactivating it?
If it does come from Link Library, I will need more information than this to be able to identify and fix this issue.
The best way to see where the problem is coming from is to activate the WordPress debug log. This is done by editing your site wp-config.php file and locating the line for WP_DEBUG.
define( ‘WP_DEBUG’, false );
By default, this line is usually set to false. You should make it true, but also add two lines so that debug messages only appear in the debug.log:
define( ‘WP_DEBUG’, true );
define( ‘WP_DEBUG_DISPLAY’, false );
define( ‘WP_DEBUG_LOG’, true );
This will create a file called debug.log in your site’s wp-content folder. Look in that file and send me the messages that it contains. If you already had a debug.log file before and it is quite large, you can just delete it to get a fresh start, then do what is needed to get the PHP notice to appear again.
I develop my plugins on an installation with all warnings turned on and did not see this notice, but it might be related to how you have Link Library configured.