Nonames statement is correct. When you read about LAN just imagine a computer network inside of a company (to make it easy, imagine it just inside of one building). If this network uses the Internet Protocol (short form: IP, a defined “language” that computers can use to communicate with each other, not only in what we call “the internet”), this in fact is an IP network. The exchange of data works exactly like it does in the internet.
So if we talk about “Voice over IP” or “IP telephony” respectively, it doesn’t mandatorily mean that the global internet is involved in data exchange.