Photoshop Libraries are a panel which is linked to Adobe Creative Cloud for storing assets.
It used to be that you could create your own libraries and drag and drop your own files into them but this no longer seems to work.
A Better Way to Store Colour Lookup Tables
You can now store Colour Lookup Tables in your Photoshop Library. The big advantage of doing this is that all the adjustment layers that you have created to produce the Colour Toning effect are saved, and when you add the effect back from the library it comes over as it was saved with all the layers intact.
Group all the adjustment layers you want to save into a Group and name this with the file name you want to keep. Drag the folder into the folder in your Library Panel to save it. To use it drag it onto a new image while holding down the OPTION key on a Mac or the ALT key on a PC. This is now available as a Group containing all the adjustment layers in an editable form. Note that it does not work if you just drag as this imports it as a Smart Object which does not work and is not editable. (Ref 2:30).