When you create a Lyris Site (in the Server Admin menu), you define the host name that Lyris Site should identify itself as. Then, when Lyris receives mail for that site, it will use that name as the From: and Reply-To: names in the responding email.
Lyris supports multiple sites, which allows it to appear to the user as if several machines are each running Lyris, and that each site (for instance, different companies) have their own Lyris server. For this reason, when mail comes in to Lyris, Lyris needs to decide on behalf of what site the mail is for, and use the appropriate Reply-To: and From: address for that site.
So, it is very important that you fill in the correct machine name for each site, so that Lyris identifies itself correctly.