The LAN is Local Area Network.
Basically inside your house or business.
ISP->Modem/router->2 PC's.
The 2 PC's and part of the router a "LAN".
The ISP is just concerned about what happens outside your house, and up to the 'modem'.
And you can have a LAN with no service from an ISP at all. It will just allow comms between local systems, but it is a LAN.
Local.