You do not need to give it internet access for LAN mode to function, but you lose a LOT of features that the cloud app and mobile app give you. For example, you can no longer do anything with the camera in LAN mode, even from the official Bambu Studio app. So no timelapses or ability to check in on it from even just elsewhere in my house.

There's also other limitations of it in features I don't really use, for example IIRC the RFID stuff they do with their print spools stops working.