To give an external user access to an entire SharePoint online library requires the following:
URL of the library that needs to be shared
Email address of the external user
Then you need to
For the 365 tenant check Azure active directory, to see if the external user already has a Guest account (if you can't do the following steps, you can share just one file from the library with the user, have them view it, and this creates the Azure account, once they've done it).