What is the difference between hall and foyer and lobby ?Feel free to just provide example sentences.

I'd say "hall" is most often used as a short version of "hallway"

"Where's your bathroom?" "Just down the hall."

However, it can also be used to describe a large open room.

"The dining hall was massive."

"Foyer" is a term I don't hear often in my own life, but I know it's often used to describe the entrance room to a house or building.

"Please leave your shoes in the foyer."

However, it's also ok to just call that entrance room a "front room," "front hall," and in some cases, some may just say "by the door." For example:

"Please leave your shoes in the foyer."
"Please leave your shoes in the front room."
"Please leave your shoes by the door."

"Lobby" is a term that I often hear used to describe public buildings:

"The front lobby of the hospital was large and crowded."

It's rarely, if ever used, when describing a house.

Hope this helps! : )