When outbound notification is setup for certificate, You would receive notifications via email if the below scenario's matches
1.While checking lifecycle manager>locker>certificates, There are certificates which are due to expire/expired.
2.The certificates are replaced but still old certificates are present in the locker>certificates
Aria suite lifecycle manager 8.x
Make sure the certificates that is due to expiration is removed from LCM locker post replacing the certificate for the product
To replace certificate of a product Replace certificate for VMware Aria Suite Lifecycle products