I was recently trying to setup a LAN multi-player game between myself and a friend by creating a game with the Visibility: Friends setting. After creating the game, the second computer was unable to see it in the lobby browser. After almost an hour of trying to figure out what the problem was and having no luck fixing it I decided to instead just make a public but password protected game and setup the match that way.
After the match I tried looking into it more and noticed my friend was showing as offline even though he was clearly signed in and online on the other computer. As soon as I took his steam client out of family view mode he appeared as online to me so I tried setting up a game again and this time it worked no problem.
So, if you're encountering issues trying to setup a multi-player game in Age of Empires II: HD, make sure none of the steam clients are in family-view mode