Looks like you already got some good answers

A "lobby" is always a large room around or near the entrance to a building. Usually it is a public building. Often, a hotel has a lobby, and a theater has a lobby. But our house doesn't have a "lobby." And a lobby is not a "long, narrow space." Confusingly, "hall" has two different definitions. A "hall" can be long, narrow passageway or corridor. Schools have halls. Hospitals have halls. "Go down that hall, and the cafeteria is near the end, on the right. But a "hall" can just be any big room--or even an entire building, particularly at a university, or a big British estate. "At the University of Wisconsin, Bascom Hall is at the top of the hill, with a statue of Lincoln in front." "In the novel, 'The Wind in the Willows,' Mr. Toad lives in Toad Hall." So it is correct to say that a lobby is a kind of hall, but not all halls are lobbies.

The distinction between the two is confusing because ‘hall’ is used in a general sense to mean a large room, as in a ‘concert hall’, or a school hall, which is the room in which all the students and teachers can congregate. It can also be used for a smaller room where meetings are held. The first definition of hall is incorrect ; the ‘long narrow space that leads to a room is a ‘hallway’ or ‘corridor’, not a ‘hall’. The first definition of ‘lobby’ is correct, and applies to large buildings, for example, a block of offices, a large hotel, a theatre, cinema, etc, or a large public building. The lobby is where a reception desk is usually found.

Hi. Yes I would say the first explanation is correct. Think of it this way, I would walk into the hotel lobby from the street, check in, then walk down the hall to my room. I would think the first room you enter when it is a business, e.g a hotel or an office, would be a lobby, however the first room you enter in somebody’s private home would be a hall. Does that help?

The first explanation was correct :)