Host is an authoritative player, there is one host per channel. You need to approach it from IRC's POV.
In IRC you connect to the server, and you are not in any lobby. You are just connected. You can receive PMs from other users, but that's about it. You can also join a chat room. First person to join a chat room is automatically designated as the channel's operator. Same with TNet -- first person to join is the "host".
With TNet if the host leaves, another player is automatically designated to be the "host", so there is always a host player in the channel. It's all seamless.
Lobby server is an optional component in TNet. Lobby server is like Unity's Master Server -- think of it as an advertisement place for servers. Servers register with the Lobby, and users that connect to the lobby can retrieve this list of servers, then connect to the server of your choice.
For example take World of Warcraft as a template. Lobby Server would handle player authorization and would give the player a list of individual servers, with the number of players in each server. The player chooses one server, and hits Connect.
Once connected to the server, the player can now join a channel. For example going into Ironforge would join the Ironforge channel. Instancing would be done the same way. Too many players in the Ironforge channel? Join Ironforge #2. Players in the same channel can see and communicate with one another.