If you go to outlook.com and login with the Microsoft account you use on your phone, then go to the upper right and click your name, select account settings. On the left menu now go to Permissions then Manage your accounts. You should see linked accounts like Facebook, Twitter, Linkedin if you have them. If Facebook is not there, you need to add it and give permission for them to be linked. If it is there, you may want to try and remove it and add it back again and then give it a little time to sync and see if that works. Hope that helps.
Note the above only addresses the Me tile and People hub notifications and updates, not lock screen or toasts as hopmedic mentioned, those are dependent on the Facebook app.