Only Modern (or Metro, as they used to be called) apps can display notifications on the Windows 8/8.1 lock screen, and Outlook 2013 is not one of them; thus, it can't directly display those notifications.

As a workaround, you can configure the same email account in the Mail app: it will then display the proper notifications when messages arrive, even if you actually use another program (Outlook) to read them.

If you are using an Exchange mailbox, Mail has full Exchange support: just add your account to the app and it will autodiscover your server settings and sync your mailbox just like Outlook does. This will also sync your calendar and contacts, thus you will also get calendar notifications on the lock screen.

If you are using another mail server, you'll instead have to configure it in Mail as an IMAP account.

Only Modern (or Metro, as they used to be called) apps can display notifications on the Windows 8/8.1 lock screen and Start menu, and Outlook 2013 is not one of them; thus, it can't directly display those notifications.

As a workaround, you can configure in the Mail app the same email account you are using in Outlook: Mail will then display the proper notifications when messages arrive, even if you actually use another program (Outlook) to read them.

If you are using an Exchange mailbox, Mail has full Exchange support: just add your account to the app and it will autodiscover your server settings and sync your mailbox just like Outlook does. This will also sync your calendar and contacts, thus you will also get calendar notifications.

If you are using another mail server, you'll instead have to configure it in Mail as an IMAP account.