I'm an Australian, so speak British English. To me, a lounge or lounge room, less commonly called a sitting room, is a room containing a lounge suite (set of soft/comfy furniture) where one quietly relaxes with a companion, knitting or crochet, a book, or TV, and on more formal occasions invites guests to relax and socialise with us. If there is a fireplace in the room it would be used often during cold weather, especially in the evenings, less often and usually only on more formal occasions during warm/hot times of year.
A living room is a multi-purpose, communal room. It's where friends chat around a table, eat snacks or meals, the children play, and the more noisy activities occur. We live in a very small house so the living room is the main room in the house, where we cook, eat, talk, socialise, read, use as an office and computer room, do crafts, and most everything else except sleep or wash.
That said, names given for the main rooms in a house are not set in stone. They will depend on the number of rooms available in the house for various activities. And families will tend to use whatever room names have been traditionally used in their family group.