It may be possible to recover lost or deleted emails in Outlook live account.
Here's a list of things you can do to attempt to recover them:

1. Check for all your emails in the Deleted Items folder.
2. Search for lost emails in the Recoverable Items folder.
3. Check if the email is in any other folders.
4. Look for any rules you might have set up to move emails to a different folder.
5. Look for the email in any other accounts it may have been forwarded to.