The Domain Name of a computer that has the LabTutor Server on it is ignored when determining the URL (Web Address) for the LabTutor Server - the LabTutor Server's URL is always just the Computer Name.
However having the LabTutor Server Computer on a Domain will cause a small issue when initially installing the LabTutor Server - the shortcut the Installation creates will include the Domain Name as part of the URL, even though this is the incorrect URL, causing the shortcut to send you to the wrong URL:
This will create a shortcut with the URL https://tom-pc.example/AdminPages when the LabTutor Serer is installed,when the correct URL is https://tom-pc/AdminPages
To correct this, manually type the correct URL into Internet Explorer, and click the 'Yellow Star' at the top-right of Internet Explorer and click 'Add to Favourites'. Then click the Yellow Star again and drag-and-drop the new Shortcut onto your desktop. Delete the old LabTutor Server Shortcut.