The no-reply email is the LMS server email address. This is the "real" email for the server through which the email notification is being sent. The email address that you put into the "From/Reply to" box is who the email notification is being sent for, and it is who the reply email will go to if the recipient replies to the email notification.
If the system marked your "From/Reply to" email address as the only "from" address, the receiving server will block it because it is not the real email address for the server, and will appear to the receiving server to be a malicious attempt at covering up the real server email.
The "on behalf of" is the LMS server telling the receiving server that the email is trustworthy.