Lobby- entry room/space for a large building. A hotel lobby has the check-in desk. A company lobby might have a security desk or welcome area. Sometimes there are seating areas but typically lobbies are for passing through to a different destination in the same building
Foyer- an entry room in a home/ house. May also have seating but usually for easy removal of shoes, not for lingering
Hall- a corridor, a long "room" that connects other rooms. It can also refer to very large rooms, like a dance hall or dining hall, or as a formal way to say room.
Lounge- a room for lounging (sitting, resting), similar to a living room or a private library or smoking room