If the user is not in the same domain the easiest way would probably be to add a local user to the server that your colleague can use.
As far as I can tell, a user connecting to ArcGIS Server via a Local (LAN) connection must be a domain user. I added my own domain account to the agsuser group which is why it works for me (I did this about three years ago which is why I didn't initially remember how logging into AGS works).
If the user is not in your domain, you could use the Internet method to connect (which does require a user name and password).
UPDATE: There is a hacky workaround to this (The Abbott of Monkseato already provided this solution, but I wanted to add the information here as well). Since you have a domain user trying to connect to a local group on a non-domain server, this is more of a network issue than an ArcGIS Server issue.
I asked a question on ServerFault and their response was that you can either:
- Add a local account with the same username and password as the domain user trying to connect
- Add the server to the domain